Differentiate with respect to , where .

To find: differentiation of with respect to

Let u =

Put x = cos θ

⇒ u = θ

⇒ u = cos^-1 x

Differentiating both sides with respect to x:

Put x = sin θ ⇒ θ = sin^-1 x

Differentiating both sides with respect to x:

Now,

Hence, the differentiation of with respect to