I am supposed to solve the following using implicit differentiation.
$\sin\left(\frac{x}{y}\right)+\ln(y)=xy$
This is what I have so far:
$\cos\left(\frac{x}{y}\right)\frac{d}{dx}\left(\frac{x}{y}\right)+\frac{d}{dx}\big(\ln(y)\big)=y+x\frac{dy}{dx}$
My problem here is differentiating the fraction as well as the $\ln y$, especially since $\ln y$ does not contain $x$ to differentiate towards.
Thanks for your help in understanding this.