How do you find the derivative of (arctan x)^3?

Mar 16, 2016

You can find it like this:

Explanation:

$f \left(x\right) = {\arctan}^{3} \left(x\right)$

$\frac{d \left[\arctan \left(x\right)\right]}{\mathrm{dx}} = \frac{1}{\left({x}^{2} + 1\right)}$

So you apply the chain rule:

$f ' \left(x\right) = 3 {\arctan}^{2} \left(x\right) \times \frac{1}{\left({x}^{2} + 1\right)}$

$f ' \left(x\right) = \frac{3 {\arctan}^{2} \left(x\right)}{\left({x}^{2} + 1\right)}$