​ Find dy/dx of y = sin^-1(2x√(1 - x^2)), -1/√2 < x < 1/√2 ​

Question

Find \(\frac{dy}{dx}\) of y = sin^-1(2x√(1 - x²)), - \(\frac{1}{\sqrt2}\)< x < \(\frac{1}{\sqrt2}\)

Answer 1

Let x = sinθ, 

⇒ θ = sin^-1x