If y = tan^–1 x, show that (1 + x^2) d^2y/dx^2 +2x dy/dx= 0.

Question

If y = tan^–1 x, 

show that (1 + x²) \(\frac{d^2y}{dx^2}+2x\frac{dy}{dx}\)= 0.

Answer 1

Formula: –

Given: –

Y = tan^–1x

Differentiating w.r.t x

\(\frac{dy}{dx}=\frac{d(tan^{-1}x)}{dx}\)

Using formula(ii)

Again Differentiating w.r.t x

Using formula(iii)

\((1+x^2)\frac{dy}{dx}+2x\frac{dy}{dx}\)=0