Question

if x=ylog(xy)then dy/dx=?

Answer 1

Hope it will help you

Answer 2

Answer:

$\frac{x-y}{x(1+log(xy))}=\frac{dy}{dx}$

Step-by-step explanation:

$x=ylog(xy)$

Differentiating with respect to x, we get

$1=y{\times}\frac{1}{xy}(x\frac{dy}{dx}+y)+log(xy){\times}\frac{dy}{dx}$

$1=\frac{dy}{dx}+\frac{y}{x}+log(xy)\frac{dy}{dx}$

$1-\frac{y}{x}=\frac{dy}{dx}(1+log(xy))$

$\frac{x-y}{x}=\frac{dy}{dx}(1+log(xy))$

$\frac{x-y}{x(1+log(xy))}=\frac{dy}{dx}$

which is the required solution.