Implicit Differentiation Problem

Question

I have this problem: $\:3x^2-10x^2\ln \left(y\right)=e^{2y}$

I end up with this: $\left(6x-\left(10x^2\left(\frac{1}{y}\cdot \frac{dy}{dx}\right)+ln\left(y\right)\cdot 20x\right)=2e^{2y}\cdot \frac{dy}{dx}\right)$

I am a little confused as to what to do as I can't leave my answer like this, can I ?

Answer 1

First, you should distribute and get rid of all of the parentheses. Next, one should get all of the $dy/dx$ terms on one side and all of the terms that do not include $dy/dx$ on the other side. Then, solve for $dy/dx$.