Question

For f(x)= e^cos(x), find f’(pi/2)

Answer 1

-1.

Explanation:

f(x) = e^cosx

Using the Chain Rule:

f'(x) = -sinx e^cosx

So

f'(pi/2) = -sin(pi/2) * e^cos(pi/2)

= -1 * e^0

= -1.

Answer 2

`f(x)=e^(\cos(x))\implies \cfrac{df}{dx}=\stackrel{ \textit{chain rule} }{\left[ e^(\cos(x)) \right][-\sin(x)]} \\\\\\ \left. \cfrac{df}{dx} \right|_{x=(\pi )/(2)}\implies \left[ e^{\cos\left( (\pi )/(2) \right)} \right]\left[ -\sin\left( (\pi )/(2) \right) \right]\implies e^0 (-1)\implies \text{\LARGE -1}`