Question

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

Answer 1

`f'(x)=(3arctan^2(x))/((x^2+1))`

Explanation:

`f(x)=arctan^3(x)`

Apply the chain rule:

`f'(x)=3arctan^2(x).(d(arctanx))/(dx)`

`=3xx1/((x^2+1)).arctan^2(x)`

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