If xsqrt(1 + y) + ysqrt(1 + x) = 0. Then how will you prove that dy/dx = -1/(1 + x)^2??

1 Answer
Jul 24, 2017

dy/dx=-1/(x+1)^2

Explanation:

xsqrt(1 + y) + ysqrt(1 + x) = 0

xsqrt(1 + y)=-ysqrt(1 + x)

x^2*(1 + y)=(-y)^2*(1 + x)

x^2*(1 + y)=y^2*(1 + x)

x^2 + x^2*y=y^2+y^2*x

x^2 -y^2=y^2*x-x^2*y

(x+y) * (x-y) = -xy * (x-y)

x+y = -xy

x = -xy-y

x = -y* (x+1)

y=-x/(x+1)

dy/dx=[-1*(x+1)-(-x)*1]/(x+1)^2

dy/dx=-1/(x+1)^2

1) I solved this equation for y.

2) I differentiated both sides.