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

Question

2097 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-28T18:19:23

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

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

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

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