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What is the derivative of #f(x) = cos( sin( x ))#?

Answer 1

Isaiah Allen

#f'(x)=-sin(sinx)*cosx#

#f'(x)=-sin(sinx)*(sinx)'=-sin(sinx)*cosx#

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Answer 2

Cameron Alexander

To find the derivative of ( f(x) = \cos(\sin(x)) ), you would use the chain rule.

[ \frac{d}{dx}(\cos(\sin(x))) = -\sin(\sin(x)) \cdot \cos(x) ]

This is obtained by taking the derivative of the outer function (\cos(\cdot)), which is (-\sin(\cdot)), and multiplying it by the derivative of the inner function (\sin(x)), which is (\cos(x)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.