Question

How do you find the derivative `h(x)=x^2arctanx`?

Answer 1

`h'(x) = x^2/(x^2+1)+2xarctan(x)`

Explanation:

`h(x) = x^2arctan(x)`

Apply the product rule.

`h'(x) = x^2 * d/dx arctan(x) + d/dx x^2 * arctan(x)`

Apply standard differential and power rule.

`h'(x) = x^2 * 1/(x^2+1) + 2x * arctan(x)`

`= x^2/(x^2+1)+2xarctan(x)`