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How do you find the derivative of #f(w)=3cos(w^2)#?

Answer 1

Cameron Alexander

#=-6wsin(w^2)#

#f'(w)=3(-sin(w^2)*2w#

#=-6wsin(w^2)#

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Answer 2

Emilia Aguilar

To find the derivative of ( f(w) = 3\cos(w^2) ), you can use the chain rule, which states that if ( g(x) ) and ( h(x) ) are differentiable functions, then the derivative of ( g(h(x)) ) with respect to ( x ) is ( g'(h(x)) \cdot h'(x) ). Applying this to our function:

( f'(w) = \frac{d}{dw} (3\cos(w^2)) = -6w\sin(w^2) )

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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.

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