Question

if ylogx = x-y , prove that
dy/dx = logx/(1+ logx)^2​

Answer 1

y log x=x-y

Y(1+ log x) =x

Y=x/(1+logx) by quotient rule

dy/dx=[(1+log x) 1-x(0+1/x)]/(1+logx)^2

=(1+ logx - 1)/(1+log x) ^2

=log x/(1+logx)^2

Answer 2

Hope it is helpful............