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

##### 1 Answer

#### Explanation:

The chain rule allows us to take the derivative of a composition of two or more functions. For two functions:

We can see that the function

By the chain rule, we first need to take the derivative of the outermost function and work our way in. It's like taking the function apart layer by layer until we get all the way through.

First, we take the derivative of the tangent function, which is

Next, we take the derivative of the

Lastly, we take the derivative of

This can also be written as: