Question

Differentiate the following w.r.t.x:
${\tan }^{-1}(3x^2+2)$

Answer 1

Let $y={\tan }^{-1}(3x^2+2)$

Differentiating w.r.t. x, we get,

$\frac{dy}{dx}=\frac{1}{1+(3x^2+2{)}^2}\left(6x\right)$

$\frac{dy}{dx}=\frac{6x}{1+(3x^2+2{)}^2}$