Find dy/dx , if y = sin^(-1)(2x/1+x^2). ​

Question

Find \(\frac{dy}{dx}\), if y = sin^-1\((\frac{2x}{1+x^2}).\)

Answer 1

 Let x = tan θ

⇒ θ = tan^-1 x.

Now,

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

\(\frac{dy}{dx}=2.\frac{1}{1+x^2}\)

\(=\frac{2}{1+x^2}\)