Question

Differentiate the following expression $w.r.t.x$
$y={\csc }^2\left(x^2\right)$

Answer 1

Given,

$y={\csc }^2\left(x^2\right)$

Now differentiating both sides with respect to $x$ we get,

$\frac{dy}{dx}=2\csc \left(x^2\right).(-\csc x^2.\cot x^2).\left(2x\right)$

or, $\frac{dy}{dx}=4x{\csc }^2\left(x^2\right)\cot x^2$.