Find dy/dx, when: x2 + y2 = log( xy) The answer: y(1 - 2x2 ) / x (2y2 - Maths - Continuity and Differentiability

Question

Find dy/dx, when:

x2 + y2 = log( xy)

The answer: y(1 - 2x2 ) / x (2y2 - 1)

Priyanka Kedia · Accepted Answer

x2+y2=logxyDifferentiating on both side w r t
 x, we get,2x+2ydydx=1xyxdydx+y⇒2x+2ydydx=1ydydx+1x⇒2ydydx-1ydydx=1x-2x⇒dydx2y2-1y=1-2x2x⇒dydx=y1-2x2x2y2-1