How do you differentiate $f (x) = sin (x^{2} cos x)$ $f(x)=sin(x^2 cos x)$ 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 $(-x)$

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

How do you differentiate f(x)=sin(x^2 cos x) f(x)=sin(x2cosx)f(x)=sin(x^2 cos x) using the chain rule?