if x(root)1+y + y(root)1+x prove dy/dx = -1/(1+x)2 - Maths - Continuity and Differentiability

Question

if x(root)1+y + y(root)1+x prove dy/dx = -1/(1+x)2

Varun.Rawat · Accepted Answer

We have,     x1+y + y1+x = 0⇒x1+y = -y1+x⇒x21+y = y21+x⇒x2 + x2y = y2 + xy2⇒x2-  y2 + x2y - xy2 = 0⇒x-yx+y + xyx-y = 0⇒x-yx+y+xy = 0⇒x+y+xy = 0          as x≠y, so x - y = 0⇒y+xy = -x⇒1+xy = -x⇒y = -x1+x ⇒dydx = -1+x × 1 - x×11+x2⇒dydx = -11+x2