Question

How do you differentiate `arctan(e^x)`?

Answer 1

`e^x/(1+e^(2x))`

Explanation:

The derivative of `arctan(x)` is:

`d/dx(arctan(x))=1/(1+x^2)`

So, in order to differentiate `arctan(e^x)`, we will need to use the chain rule:

`d/dx(arctan(u))=1/(1+u^2)*(du)/dx`

For `u=e^x`, we see that

`d/dx(arctan(e^x))=1/(1+(e^x)^2)*d/dx(e^x)=e^x/(1+e^(2x))`