How do you differentiate #f(x)=cot(1/e^x) # using the chain rule?

1 Answer
Feb 17, 2016

Answer:

#1/e^(x)csc^2(1/e^x)#

Explanation:

To do this we need the chain rule.

First we find the derivative of the function inside the cot function. Remember #1/e^x=e^-x#

#d/dx(e^-x)=-e^(-x)=-1/e^(x)#

Also the derivative of #cot(x)#:
#d/dxcot(x)=-csc^2(x)#

The chain rule states that: #d/dxf(g(x))=g'(x)f'(g(x))#
So we take the derivative of the inside and multiply it by the derivative of the outside. We found the derivatives, we just need to multiply to get:

#1/e^(x)csc^2(1/e^x)#