Question

What's the derivative of `arctan(8^x)`?

Answer 1

`(8^x ln 8)/(1+8^(2x))`

Explanation:

Let u = `8^x=e^(x ln 8) and y = arc tan 8^x`.
`d/dx(y)=d/du(y)d/dx(u)`.
`=1/(1+u^2)(ln 8 e^(x ln 8))`
`= (8^x ln 8)/(1+8^(2x))`