Question

What is the derivative of `(arctan x)^3`?

Answer 1

`(3arctan^2(x))/(1+x^2)`

Explanation:

The rule for deriving the power of a function states that

`d/dx f^n(x) = n f^{n-1}(x) * f'(x)`

In your case, `f(x)=arctan(x)`, and thus `f'(x) = 1/(1+x^2)`

Appling the rule with `n=3` gives us

`d/dx arctan^3(x) = 3arctan^2(x) * 1/(1+x^2)`