If xy log (x+y)=1 prove that dy /dx = -y (x^2y+x +y)/x (xy^2+x+y) Share with your friends Share 0 Priyanka Kedia answered this Given, xylogx+y=1 .....1Differentiate with respect to x, xddxylogx+y+ylogx+yddxx=ddx1⇒xyddxlogx+y+logx+yddxy+ylogx+y1=0⇒xy1x+y1+dydx+logx+ydydx+ylogx+y=0⇒xyx+y+xyx+ydydx+xlogx+ydydx+ylogx+y=0⇒xyx+y+xyx+ydydx+xxydydx+yxy=0 from equation 1, logx+y=1xy⇒xyx+y+xyx+ydydx+1ydydx+1x=0 ⇒xyx+y+1x+xyx+y+1ydydx=0⇒x2y+x+yxx+y+xy2+x+yyx+ydydx=0⇒dydx=-x2y+x+yxx+yxy2+x+yyx+y⇒dydx=-yx2y+x+yxxy2+x+yHence proved. 2 View Full Answer anjineyulu answered this take xy as u and log(x+y)as v and diffrentiate after diffrentiating take log(x+y) as 1/xy and u will get the answer 0
