Question

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

Answer 1

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

Explanation:

Use the Chain Rule and the facts that `d/dx(arctan(x))=1/(1+x^2)` and `d/dx(8^{x})=ln(8) * 8^{x}` to get:

`d/dx(arctan(8^{x}))=1/(1+(8^{x})^2) * d/dx(8^{x})`

`=(ln(8)8^{x})/(1+8^{2x})`