# What is the derivative of y= tan^-1(x^2)?

The derivative of $\arctan f \left(x\right)$ is
$d \frac{\arctan f \left(x\right)}{\mathrm{dx}} = \frac{f ' \left(x\right)}{1 + {\left(f \left(x\right)\right)}^{2}}$
where $f \left(x\right) = {x}^{2}$ hence
$d \frac{\arctan {x}^{2}}{\mathrm{dx}} = \frac{2 x}{1 + \left({x}^{4}\right)}$