Question: Find the gradient of the curve $x \ln y - \frac{x}{y}=2$ at $(-1,1)$
I've done something wrong as I got the gradient to be $0$ when the answer in the back says $-0.5$
Can someone help me with this question?
edit:
I got: $1+\frac{1}{y}\frac{dy}{dx}-\frac{y-x\frac{dy}{dx}}{y^2}$
$y^2+y\frac{dy}{dx}-y-x\frac{dy}{dx}=0$
$\frac{dy}{dx}=\frac{y-y^2}{y-x}$
Substituting the values in did not get me the answer
When you differentiate you get: $$ \ln{y}+\frac{x}{y}y'-\frac{y-xy'}{y^2}=0 $$
Then substituting $x=-1,y=1$ you obtain: $-y'-(1+y')=0$ so $y'=-1/2$.