Question

Differentiate 1_x² over 1+x²​

Answer 1

Dy/Dx=-4x/(1+x²)²

Explanation:

The differential of 1_x² over 1+x²​

First of all

1_x² over 1+x²​ = (1_x²) / (1+x²​)

Let (1_x²) = u

Let (1+x²​) = v

Differential = Dy/Dx

Dy/Dx of (1_x²) / (1+x²​)

= (VDu/Dx -UDv/Dx)V²

u = (1-x²)

Du/Dx = -2x

(VDu/Dx) =(1+x²)(-2x)

V = 1+x²

Dv/Dx = 2x

UDv/Dx= (1-x²)(2x)

v² = (1+x²)²

Dy/Dx = ((1+x²)(-2x) - (1-x²)(2x))/(1+x²)²

Dy/Dx= ((-2x -2x³)-(2x-2x³))/(1+x²)²

Dy/Dx=( -2x -2x - 2x³ +2x³)/(1+x²)²

Dy/Dx=-4x/(1+x²)²