# How do you differentiate #f(x)=csce^(4x)# using the chain rule.?

##### 1 Answer

#### Explanation:

The chain rule states that when differentiating a function inside of a function, (1) differentiate the outside function and leave the inside function as is, and (2) multiply this by the derivative of the inside version.

In

Thus, since the derivative of

#f'(x)=-csc(e^(4x))cot(e^(4x))*d/dx(e^(4x))#

Don't forget to multiply by the derivative of the inside function, which is

To differentiate

The outside function is

#d/dx(e^(4x))=e^(4x)*d/dx(4x)#

Note that

#d/dx(e^(4x))=4e^(4x)#

Plug this back in to the derivative of the whole function:

#f'(x)=-4e^(4x)csc(e^(4x))cot(e^(4x))#