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

1 Answer
May 30, 2016

Answer:

#\frac{d}{dx}cos(e^x)=-sin(e^x)e^x#.

Explanation:

Chain rule says that

#\frac{d}{dx}f[g(x)]=f'[g(x)]g'(x)#.

Our #f# is the cosine and our #g# is the exponential.
The derivative of #cos# is #-sin#, while the derivative of the exponential is the exponential, so we have

#\frac{d}{dx}cos(e^x)=-sin(e^x)e^x#.