​ (i) Let y = x^sin x + (sinx)^x. Find dy/dx (ii) Given ; y = √(tan^-1x)

Question

(i) Let y = x^{sin x} + (sinx)^x. Find \(\frac{dy}{dx}\)

(ii) Given; y = \(\sqrt{tan^{-1} x}\)

(a) 2 (1 + x²) \(y\frac{dy}{dx} = 1\)

(b) (1 + x²) \(y\frac{d^2y}{dx^2} \) + (1 + x²)(\(\frac{dy}{dx}\))² + 2xy \(\frac{dy}{dx}\) = 0

Answer 1

Let y = x^sinx + (sinx)^x = u +v