How do you differentiate #f(x)=sin(x^2 cos x) # using the chain rule?

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Answer 1 · 2015-10-28T06:00:29

When you finish using the Chain Rule the derivative is

#f'(x)=-xcos(x^2cos(x))[xsin(x)-2cos(x)]#

Take the derivative of the outside

#h(x)=sin(x^2cos(x))#

#h'(x)=cos(x^2cos(x))#

Take the derivative the of the inside, use the product rule

#g(x)=x^2cos(x)#

#g'(x)=x^2(-sin(x))+2x(cos(x))#

#g'(x)=-x^2sin(x)+2xcos(x)#

Multiply the derivative of the outside and inside

#f'(x)=cos(x^2cos(x))[-x^2sin(x)+2xcos(x)]#

Factor out #(-x)#

#f'(x)=-xcos(x^2cos(x))[xsin(x)-2cos(x)]#