Question

if x √1+y - y √1+x = 0 then dy/dx

Answer 1

Step-by-step explanation:

x√(1+y) - y√(1+x)=0

x√(1+y)=y√(1+x)

squaring on both sides

x²(1+y) =y²(1+x)

differentiate w. r. t x on both sides

d/dx[x²(1+y)]=d/dx[y²(1+x)]

$d/dx(uv) = u(dv/dx)+ v(du/dx)$

x²(dy/dx) +(1+y)2x=y²(1)+(1+x)2y(dy/dx)

dy/dx[x²-2y(1+x)]=y²-2x(1+y)

dy/dx=[y²-2x(1+y)]/[x²-2y(1+x)]