If log(x2+y2)=2tan-1(y/x), then show that dy/dx=x+y/x-y - Maths - Continuity and Differentiability

Question

If log(x2+y2)=2tan-1(y/x), then
show that dy/dx=x+y/x-y

Vipin Verma · Accepted Answer

log(x2+y2) = 2tan-1yxDifferentiating both sides with respect to
x,we get1(x2+y2)×(2x +2ydydx)
=2×11+(yx)2×xdydx-yx2Or 1(x2+y2)×(2x +2ydydx) =
2×x2x2+y2×xdydx-yx2Or (2x +2ydydx) =2×(xdydx-y)
Or x+ydydx =xdydx-y Or dydx=x+yx-y (Hence proved)

If log(x2+y2)=2tan-1(y/x), then show that dy/dx=x+y/x-y.

If log(x²+y²)=2tan^-1(y/x), then show that dy/dx=x+y/x-y.