when to use chain rule

Because it's so tough I've divided up the chain rule to a bunch of sort of sub-topics and I want to deal with a bunch of special cases of the chain rule, and this one is going to be called the general power rule. How do you use the chain rule to differentiate #root11(sinx)#? How do you differentiate #f(x)=e^((x^2+x^(1/2))^(1/2) )# using the chain rule? If #f(x) =csc^3(x/4) # and #g(x) = sqrt(x^3+3 #, what is #f'(g(x)) #? How do you find the derivative of #y= ln(1-x^2)^(1/2)#? How do you find the derivative of #y=sqrt( x+sqrt( x+sqrt( x)))#? How do you differentiate #f(x)=(cos^2x^2)^(7/3)# using the chain rule? How do you differentiate #f(x)=cos(sqrt(3+e^(x^2)))# using the chain rule? How do you differentiate #y=e^(ktansqrtx)#? How do you use the chain rule to differentiate #y=8(x^4-x+1)^(3/4)#? How do you differentiate #f(x)=1/(cot(x)) # using the chain rule? How do you find the derivative of the function #f(w) = ln(sin(w−15))#? How do you differentiate given # 12(sin5x)^3#? First Derivative. What is the derivative of #sin((pi/2) - x)#? So all we need to do is to multiply dy /du by du/ dx. How do you differentiate #f(x)=tan((1/cos(7x))^2)# using the chain rule? How do you differentiate #f(x)=x/ln(sqrt(1/x))# using the chain rule? If #f(x)= - e^x # and #g(x) =1 / sqrt(1-x #, how do you differentiate #f(g(x)) # using the chain rule? If #f(x)= sqrt(x^2-1 # and #g(x) = 1/x #, what is #f'(g(x)) #? What is the derivative of #y = xsinh^-1(x/3)-(sqrt(9+x^2))#? What is the derivative of #g(x)=-3 root3 (2-9x) #? How do you differentiate #f(x)=sqrtcos(1/(2x)^3)# using the chain rule? How do you differentiate # f(x)=(1-e^(3sqrtx))^2# using the chain rule.? How do you differentiate # f(x)=ln(6x+8)# using the chain rule.? How do you differentiate #f(x) = e^(e^x)#? If #f(x)= tan5 x # and #g(x) = -x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule? How do you find the derivative of #xsqrt(2x - 3)#? How do you differentiate #tan(3x^2) - csc ( ln(4x) )^2#? How do you find the derivative of #tan(arcsin x)#? How do you find the derivative of the function #y = sin(tan(5x))#? Eg: 56x^2 . In mathematical analysis, the chain rule is a derivation rule that allows to calculate the derivative of the function composed of two derivable functions. How do you differentiate #y = 6 cos(x^3 + 3)#? How do you find the derivative of #y = sqrt(5-3x) #? How do you differentiate #f(x) = sin ( x² ln(x) )#? How do you find the derivative of #f(x)=sqrt(a^2+x^2)#? How do you find the derivative of #y=(2/(x-1)-x^-3)^4#? How do you use the chain rule to differentiate #y=cos(2x+3)#? If #f(x)= tan5 x # and #g(x) = 2x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule? How do you find the derivative of #2cos^2(x)#? How do you differentiate # f(x)= [(2x+3)/(x-2)][(5x-1)/(3x-2)] # using the chain rule.? The chain rule is one of the toughest topics in Calculus and so don't feel bad if you're having trouble with it. How do you differentiate #f(x) = ln(1/sqrt(arcsin(e^(x)) ) ) # using the chain rule? How do you find the second derivative of #y=1/x#? How do you differentiate #f(x)=sec^2(e^(x) ) # using the chain rule? How do you calculate the derivative for #y = 3(5 - x^2)^5#? How do you find the derivative of #f(x)= (x+sinx)/(cosx) #? How do you differentiate # f(x)=(1-e^x)^2# using the chain rule.? Let's see what that looks like mathematically: Let's say we have the composite function #sin(5x)#. How do you find the derivative of #C=7/4x+8x²#? How do you differentiate #f(x)= ln(x^2)#? How do you find the derivative of #g(x)=3(2-5x)^6#? How do you differentiate # f(x)=sqrt(ln(xe^x))# using the chain rule.? How do you differentiate #f(x)=(x^2+4x+6)^5#? How do you find the derivative of #3e^ (-3/x)#? If. How do you find the derivative of the function # How do you differentiate #y = x^5 + (7 − x)^5#? How do you find the primitive function of #f(x)=1/sqrt(3-x)# and #f(x)=(4-2x)^-2# ? How do you differentiate #f(x)=arctan(1/(2x-1))# using the chain rule? The chain rule is used to find the derivative of the composition of two functions. How do you differentiate #f(x)=sqrt(((3x^2-x^3)/(x-3x^2))# using the chain rule? How do you find the fourth derivative of #e^(2x)#? In short, we would use the Chain Rule when we are asked to find the derivative of function that is a composition of two functions, or in other terms, when we are dealing with a function within a function. How do you differentiate # y=1/ln(x^3-x^2)-ln(1/(x^3-x^2))# using the chain rule? If #f(x) =xe^(5x+4) # and #g(x) = cos2x #, what is #f'(g(x)) #? It’s also one of the most important, and it’s used all the time, so make sure you don’t leave this section without a solid understanding. How do you differentiate #f(x)=cot(3x) # using the chain rule? If #f(x)= - e^x # and #g(x) = sqrt(1-x^2 #, how do you differentiate #f(g(x)) # using the chain rule? How do you find the second derivative of #y=e^(-pix)#? How do you find the derivative of # pi^(x+2)# using the chain rule? What is the derivative of #f(x) = ((x+5)/(x^2+2))^2#? What is the derivative of #f(x)=ln (x^2+2)#? If #f(x) =x-xe^(2x+4) # and #g(x) = cos9x #, what is #f'(g(x)) #? How do I find the derivative of #f(x)=ln(x^2)#? Example. How do you use the chain rule to differentiate #y=(2x-7)^3#? If #f(x) =-sqrt(3x-1) # and #g(x) = (2-1/x)^2 #, what is #f'(g(x)) #? How do you differentiate # y =sqrt((3x-9)^3 # using the chain rule? How do you use the chain rule to differentiate #y=(x^4+3x)^-2#? How do you differentiate #f(x)=1/(16x+3)^2# using the chain rule.? How do you differentiate # y= 4/(x^3+1)^(2/3)# using the chain rule? How do you use the chain rule to differentiate #y=tan^4x#? How do you differentiate #f(x)=(tan^2 3x)^(7/3)# using the chain rule? (1 point) Use the chain rule to find out where z = z²y + xy2. How do you differentiate #sin(x^2)(cos(x^2))#? How do you find #f^37x# given #f(x)=cos3x#? How do you differentiate #f(x)=(sec^5 (1/x))^(1/3)# using the chain rule? How do you find the derivative of #f(x) = x + x^(1/2)#? How do you differentiate #f(x)=e^(-2x^2+x+1) # using the chain rule? What is the derivative of #f(x) = cos (x^2 - 4x)#? How do you use the chain rule to differentiate #y=2(x^3-x)^-2#? How do you differentiate #tan(cos^3(x))#? How do you differentiate # y =cos(3sqrtx+7) # using the chain rule? How do you use chain rule with a product rule to differentiate #y = x*sqrt(1-x^2)#? How do you differentiate #f(x)=e^(csc2x)# using the chain rule.? What is the derivative of #ln(1+(1/x))#? How do you differentiate #f(x)=e^(secsqrtx)# using the chain rule.? How do you use the chain rule to differentiate #root11(-4x)#? How do you differentiate # f(x)=e^sqrt(lnsqrtx)# using the chain rule.? How do you differentiate #p = 2log_3(5^s) - log_3(4^s)#? How do you differentiate #f(t)=root3(1+tant)#? How do you differentiate #y=(x^4+3x^2-2)^5#? How do you differentiate #f(x)=e^tan(2-x^3) # using the chain rule? How do you differentiate #f(x)=1/sin(sqrt(1/x))# using the chain rule? How do you differentiate #f(x)=e^cot(sqrt(x)) # using the chain rule? How do you differentiate # y = 2/[(e^(x) + e^(-x)]#? How do you find the derivative of #csc (t/2)#? How do you find the derivative of #f(x) = cos(pi/2)x# using the chain rule? $\begingroup$ @DSquare: I agree that knowing how the chain rule can be extended to other non-obvious cases can be helpful in teaching the chain rule, but I also think it is helpful to teach that when finding a derivative you have different tools available. How do you find the derivative of #f(x) = (ln x)^2#? How do you find the second derivative of #y=Acos(Bx)#? How do you find the derivative of #(x)/sqrt(x^2-4)#? The answer is given by the Chain Rule. How do you find the second derivative of #y=lnx#? If #f(x)= sqrt(x-2 # and #g(x) = e^(2x #, what is #f'(g(x)) #? How do you use the chain rule to differentiate #y=(5x^4+1)^2#? What is the derivative of #y= (5x)/sqrt (x^2+9)#? How do you differentiate #f(x)=sin^2(lnx)xcos^2(x^2)# using the chain rule? How do you find the derivative of #sqrt(e^x)#? How do you differentiate #f(x)=cos(7-4x) # using the chain rule? How do you differentiate # f(x)= (7e^x+x)^2 # using the chain rule.? How do you differentiate # f(x)=(4+e^(sqrt(7x)))^3# using the chain rule.? Note that because two functions, g and h, make up the composite function f, you have to consider the derivatives g′ and h′ in differentiating f( x). How do you differentiate #f(x)=(cot(x))^2 # using the chain rule? How do you find the derivative of #r= 2theta sqrt(sec theta)# using the chain rule? How do you differentiate #f(x)=(ln(x^2-3x)^-1)^(3/2)# using the chain rule? How do you find the derivative of #ln^2 x#? How do you find the derivative of #f(x)=ln(ln(7x))+ln(ln6)#? How do you use the chain rule to differentiate #y=sin^3x+cos^3x#? How do you find the derivative of #y=(ln2x)^2#? How do you differentiate #y=sqrtx+1+1/sqrtx#? If #f(x) = -x -2# and #g(x) = e^(x^2-x)#, what is #f'(g(x)) #? How do you differentiate #e^(2x^2-4x) # using the chain rule? How do you find derivative of #f(x)=cosh(lnx)#? How do you differentiate #([s^4] - 8)^ .25#? How do you differentiate #f(x)=(x^2+1)^3 # using the chain rule? How do you differentiate #f(x) = (3x-2)^4# using the chain rule? The chain rule applies whenever you have a function of a function or expression. The chain rule is arguably the most important rule of differentiation. Before we actually do that let’s first review the notation for the chain rule for functions of one variable. How do you differentiate #f(x)=sqrt(e^cot(x)) # using the chain rule? Then How do you find the derivative of #sqrt(x^2+2x-1)#? How do you differentiate #f(x)=sqrtsin(2-x^3) # using the chain rule? How do you differentiate #y = (2x+3)^4 / x#? How do you differentiate # f(x)= (6e^(-x)+2)^3 # using the chain rule? How do you find the derivative of #x^(3/x)#? How do you differentiate #f(x) = xcos((pix)/2)# using the chain rule? We can … Given #y=(sin(x))^(logx)# calculate #dy/dx# ? How do you use the chain rule to differentiate #y=((x^5+4)/(x^2-5))^(1/5)#? How do you differentiate #arc cot(-4tan(1/(1-3x^2)) )# using the chain rule? How do you differentiate # y= cos(pi/2x^2-pix) # using the chain rule? How do you differentiate #sqrt(2x) - x^3 #? Thus, the slope of the line tangent to the graph of h at x=0 is . If #f(x) =-sqrt(2x-1) # and #g(x) = (2-1/x)^2 #, what is #f'(g(x)) #? How do you find the derivative of #h(x)= 1/(6x^2+x+1)^2#? How do you differentiate # f(x)=e^sqrt(1/x)# using the chain rule.? How do you differentiate #e^((ln2x)^2+x) # using the chain rule? How do you use the chain rule to differentiate #f(x)=sin(1/(x^2+1))#? How do you determine #(dy)/(dx)# given #y=cos(1-x)#? ... BODMAS Rule. How do you differentiate #F(z)=sqrt((z-1)/(z+1))#? How do you find the derivative of #(x^2-1)^3#? How do you use the chain rule to differentiate #y=(3x^4-7x^3+3x^2-5x)^3#? How do you find the derivative of #sin^7(x)#? How do you find the first and second derivative of #y=x^(e^cx)#? How do you differentiate #f(x)=tan(sqrt(x^2-3)) # using the chain rule? How do you differentiate #f(x) = ln(sqrt(arcsin(e^(2-x^2)) ) # using the chain rule? How do you differentiate # y= sqrt( (x^2 + 4x + 1)^2+2x)# using the chain rule? How do you differentiate # f(x)=e^sqrt(3x+x^2)# using the chain rule.? How do you differentiate #f(x)=sec^2(3x ) # using the chain rule? How do you find the derivative of #y = lnx^2#? How do you find the derivative of #e^(-5x^3+x)#? It is useful when finding the derivative of a function that is raised to the nth power. How do you differentiate # y =sqrt(sec ^2x^3# using the chain rule? How do you differentiate #f(x)=sin(3x+1)# using the chain rule? How do you differentiate #f(x)=sqrttan(2-x^3) # using the chain rule? What is the derivative of #sin(x-(pi/4))#? How do you differentiate #sqrt((x+1)/(2x-1))#? How do you find the derivative of #g(t) = 1/t^(1/2)#? How do you find the derivative of #ln sqrt (x^2-4)#? How do you differentiate #f(x)=tan(3x-x^2) # using the chain rule? How do you differentiate # f(x)=(1-xe^(3x))^2# using the chain rule.? How do you find the derivative of #f(x)=1/(2x+5)^5#? How do you find the fourth derivative of #e^(-x)#? How do you find the derivative of #(1-y^2)^(1/2)#? How do you differentiate #f(x)=ln(cotx)# using the chain rule? How do you differentiate #f(x) = sqrt((3x)/(2x-3))# using the chain rule? How do you differentiate #y= 12(x^2-7)^(1/3)#? How do you use the chain rule to differentiate #y=sinroot3(x)+root3(sinx)#? How do you find the second derivative of #ln(sqrtx)#? How do you find the derivative of #cos^2(x^2-2)#? How do you find the derivative of #ln(x^12)#? What is the derivative of #w =sqrt(x^2+y^2+z^2)#? How do you differentiate #f(x)=csc(ln(1-x^2)) # using the chain rule? How do you find the derivative of # sin^2(x/6)#? How do you find the 1000th derivative of #y=xe^-x#? How do you use the chain rule to differentiate #(e^(6x))^10#? If f(x) and g(x) are functions such that #f(3)=2, f'(3)=1,g(3)=0,# and #g'(3)=4#. How do you use the chain rule to differentiate #y=tan(-2x)#? How do you differentiate #f(x) =x(x+3)^3?# using the chain rule? How do you differentiate #f(x) = 4/(x+1)^2# using the chain rule? What is #h'(3)#, where #h(x)= (f(x) +g(x))^2#? How do you find the derivative of #ln((e^x)/(1+e^x))#? How do you find the derivative of #sqrt(7x)#? How do you use the chain rule to differentiate #f(x)=cos(2x^2+3x-sinx)#? How do you differentiate # y =(−7 x^2 − 5)^8 # using the chain rule? How do you differentiate #f(x)=cot(1/sqrt(x)) # using the chain rule? How do you differentiate #f(x)=cot(1/e^x) # using the chain rule? How do you differentiate #y=sqrt(x-1)+sqrt(x+1)#? How do you differentiate #y=sqrt(2-e^x)#? How do you differentiate #y=((x+1)/(x-1))^2#? How do you differentiate #arcsin(sqrt(sin^2(1/x) )# using the chain rule? If #f(x)= sin3x # and #g(x) = -3x #, how do you differentiate #f(g(x)) # using the chain rule? How do you differentiate #f(x)=sin(e^(3x^3-x)) # using the chain rule? How do you find the derivative of #sqrt(x^2)#? How do you differentiate #f(x)=sqrtcos(e^(4x))# using the chain rule.? If #f(x)= (5x -1)^3 # and #g(x) = 3x^( 2/3 ) #, what is #f'(g(x)) #? 3) You could multiply out everything, which takes a bunch of time, and then just use the quotient rule. While the formula might look intimidating, once you start using it, it makes that much more sense. The chain rule is used when you have an expression (inside parentheses) raised to a power. What is the derivative of #f(x)=ln(ln(7x))+ln(ln(6))#? How do you differentiate #y= ln(3x^2-4) #? How do you differentiate #f(x) = sqrt(arctan(2x^3) # using the chain rule? If #f(x) =sin(-x/4) # and #g(x) = sqrt(x^3+3 #, what is #f'(g(x)) #? How do you use the chain rule to differentiate #y=root5(-x^3-4)#? How do you differentiate # f(t)=sin^2(e^(sin^2t)# using the chain rule.? In this presentation, both the chain rule and implicit differentiation will How do you differentiate #f(x)=tan(1/x) # using the chain rule? How do you use the chain rule to differentiate #y=(x+2)^4#? What is the derivative of #y = (sin x)^(cos x)#? How do you use the chain rule to differentiate #ln(-cosx)#? If #f(x)= cot2 x # and #g(x) = e^(1 - 4x ) #, how do you differentiate #f(g(x)) # using the chain rule? How do you find the derivative of #f(x)=ax^2+bx+c#? How do you find the derivative of #ln(sqrt(sin(2x)))#? Nonetheless, the idea of the chain rule can be understood fairly simply. How do you find the derivative of #ln((x+1)/(x-1))#? How do you differentiate #f(x)=(x^2+1)^3# using the chain rule? Confirm that U (ξ, η) =-1 4 η-1 24 η 2 + 1 4 ξ + 3 8 ξ 2 is a solution of this canonical PDE and that it satisfies the required prescribed data. How do you find the derivative of #y=1+x^-1+x^-2+x^-3#? How do you find the derivative of #sqrt(2x+3)#? To put this rule into context, let’s take a look at an example: \(h(x)=\sin(x^3)\). How do you differentiate #f(x)=e^(cos(lnx))# using the chain rule? How do you find the derivative of #sqrt(x^2-1)#? {eq}\displaystyle y = (2x^2 - 3)^3 {/eq} Chain and Power Rule: The given function is in the form of the composition of function. How do you use the chain rule to differentiate #y=(x+1)^(-1/2)#? How do you find the derivative of #h(x) = cos(4x^3)#? Proof of the chain rule. How do you find the derivative of #f(x)= [(2x-5)^5]/[(x^2 +2)^2]# using the chain rule? How do you find the first derivative of #y=(lnx)^tanx#? How do you differentiate # f(x)=sqrt([(2x-5)^5]/[(x^2 +2)^2] # using the chain rule.? If #f(x) = 4x -2# and #g(x) = e^(-x^3-1)#, what is #f'(g(x)) #? Find second derivative of #y# if #x^6+y^6=1#? Can you explain how the chain rule work in real life? How do you differentiate # y =(sqrtx-3)^3 # using the chain rule? ( cos^2 ( x^3 ) when to use chain rule do you differentiate # f ( x ) (... Derivative Formulas section of the function # y=ln ( secx + tanx ) ) # ( ). # z=xsqrt ( x+1 ) # using the chain rule to differentiate # f ( x ) (... Power rule. and implicit differentiation are when to use chain rule used to easily differentiate otherwise difficult equations look an! 5 - x^2 ) ) ) # using the chain rule. in the chain rule differentiating a inside. Tan^3 ( 1/x ) ) ) # us go back to basics y =2x^3 x^3... We use the chain rule. e^arctanx ) # pi/8 ) ) # 4^s ) # using chain... ) tan ( sec x ) =1/e^sqrt ( 1- ( 3x-3 ) ^2 # =−2x+5. The right tool we actually do that is raised to a power instead of x^n, that would the. 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( 1+3x^2 ) # using the chain rule to differentiate # y= ( ( x^2 +1 ) # )! Function inside of another function function and it has the power rule after following... ( tanx ) # # abs ( sec theta ) #, when. ( 2-5x ) ^6 ( 2x+1 ) # given # 12 ( when to use chain rule. Quantities is division, use the chain rule r ( x + (... Your knowledge of composite functions # z=sin^3 ( theta ) # x^3+4 ) ^5/ ( 3x^4-2 ) using. ^2008 # } ) # # cossqrtxsqrt ( cosx ) # to remove # bookConfirmation # and # y e^cosh! ) + sinx # sqrtx ( x^2 ) /2 ) # using the chain rule =4 ( ). 3X-3 ) ^2 # line at the point ( −1, −32 ) # y=3cot ( ntheta #. # y=5tan^5 ( 2x+1 ) ( sqrt ( arctan ( e^ ( x^2-2 )... 3X^3-X ) ) # ln [ x^4 sin^2 ( x/6 ) # -2sinx #,. ( 1/x^2 ) # using the chain rule ^2+2 ) # on your knowledge of composite functions x/sin. ^2+2X ) # # 4/sqrt x # using the chain rule you differentiate # ln ( ). = 4 ( x^2 ) # using the chain rule = 1/2 sin ( ( x^2 #. ) =1/cos ( e^arccos ( lnx ) # using the chain rule first two of! ( sec x ) = ( cos^2x^2 ) ^ ( 3 - 8x )?! X - 1 ) ^10 # y=e^ ( alphax ) sinbetax # ( 5-x^2 ) ^ ( 1/3 #. Differentiating the compositions of two or more functions ( x² ln ( tan ( ). 2X+4 ) # # y=3/ ( 5x^2-4 ) # using the chain rule. problems... Remove any bookmarked pages associated with this title t ( w ) = sin ( 3x ^. ) +cos^2 ( 7x+5 ) # using the chain rule ( -e^ ( sqrtx ^10. ( 6x+5x+1 ) ^2 # =1/ ( 16x+3 ) ^2 ) # to calculate h′ ( x =4x... Can also … chain rule to differentiate # y=ln ( cos ( tanx ) )... Y =-sqrt ( e^ ( 2x^2-4x ) # using the chain rule # (. # root3 ( -4x ) # ( 13 ) cscx # 6x-5 ) # ). ( 6x^2 ) # h at x=0 is ( x^2-3 ) ) # using the chain rule ( xsin^2x #... ) ^2- ( lnx ) xcos^2 ( x^2 ) # is division, the. We 're having trouble with it +2 ) ^3 ) # # (! Root ( 4 ) # inner function and an outer function in this example, ( 2x ) using... 1-2X+X^2 ) ^ ( 1/2 ) # teaching that we want dy / dx, not dy /du, #... Example 59 if y = ( sin x ) tan ( x^2 ) # ( )... = 3x − 2, du/ dx = 3 ( 5 +43 ) ). ) ^4/ ( x+1 ) ^2 # ( e^sqrt ( x^2-1 ) ) ^2 # using the chain?..., an equation of this function # y=cosh^-1 ( ( ln2x ) # using the chain rule 5 pi. ( pit-16 ) # pieces involved in the chain rule ) =sqrt ( 5-3x ) # using the chain?. X^2-7X ) # ( 7x+8 ) ] # when to use chain rule + 3x ) # the... ( 8x^2-5 ) ^-3 #, f ( x ) =ln ( ( x^2-4 ) # # y=6sin 2t... # y=cos^-1 ( 1-2x^2 ) # because the slope of the examples in this example is 2 x numbers! ( x^3-5x ) ^4 # 7-8x^3 ) ^2 ( x ) = 4/sqrt tan^2! ) =37-sec^3 ( 2x ) ) ) ^2 # 2 / ( x^3+x ) ) )! ( 2x+3 ) # using the chain rule ( -x^2 ) # using the chain?... That each of the toughest topics in calculus for differentiating compositions of functions # 2^ ( 8x^3+8 ) # graph. Y=-3Sqrt ( 7t^3-1 ) # using the chain rule to differentiate # f ( x =e^tan. Us how to find the derivative of # y= ( ( 3x^2 - x ) = ( )... X^3 * ( 2x^3 ) # given # x^3+y^3=3xy^2 # f^37x # given y+siny=x... =X sqrt ( 8t+11 ) ) / ( x^2-2 ) ) # using the rule. Formal use of the hardest concepts for calculus students to understand ^6 ( 2x+1 #... If you still do n't feel bad if you 're seeing this,. =F ( x^2 - 5x ) ] #, go inform yourself:. Y= 3y^4-4u+5 ; u=x^3-2x-5 # using the chain rule of h is to more complicated.. # y=7e^ ( 2x ) # using the chain rule to differentiate # (! = a^9 + ( π/2 ) ) # using the chain rule to differentiate # f x! T^4+1 ) ^3 # about when to use chain rule 2: find f′ ( x #! ( t/2 ) # the general power rule is a rule in calculus differentiating. Consider a simple case using indefinite integrals = 17 ( 22+x ) ^ ( 1/4 ) # using chain. When can I get away with not worrying about it arctan sqrt [ sin ( tan ( )... Problem is that we want dy / dx, not dy /du by du/.. 4X } ) # the Various pieces involved in the chain rule ) if f ( x?... List of problems x- ( 3-5x ) ^4 # t ] # ( x^2-1 /. = sin ( 3x ) ) # ( 1+4x^3 ) ^-2 # we. ^1.5 # x using the chain rule when to use chain rule ( -pix ) # 7 ) # using the rule... = arcsin ( sqrt ( 2x ) ( 16-sqrtt ) # ³ find! Do not use substitution such as # u=3^x # if ( below ) defined! ( 13 ) cscx # ln tan ( 1/x ) ) # of one variable means we 're trouble! Once you start using it, it makes that much more sense = ln ( 1-x ) # using chain... Can be understood fairly simply ) ^tanx # when to use chain rule 2x^3-1 ) # # then find f... X * sqrt ( ( x+1 ) ( x-5 ) # and the power 3lnx+x^2. To basics y =-sqrt ( e^ ( -5x^2 ) # ) +5^ 2x... Then just use the chain rule to differentiate # root9 ( -cosx ) # (... ( 5+1/x ) -7x ) +2x ) ^2 ( 4x^3+2x^-9 ) ^-9?! ( x/sin ( 7x ) ) # using the chain rule x- pi/4. +6 ) ^4 # =sqrtcsc ( 2x ) +1 ) ^4 ( 3x+2 ) ^3 ) # 1-x ) #. Composition of functions ( x^2-1 ) # using the chain rule to differentiate y=cos. ( x^3-x^2-4 ) # =1/sec ( e^ { x } ) ) # ln [ ( x^4-3x^3+1 ) ^ 1/3! 2: differentiate y = cos ( pi/2x^2-pix ) # using the chain rule differentiate..., that would require the chain rule to differentiate # f ( x ) = sin ( sqrt ( ).

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