Implicit differentiation I have looked at several examples and I still fail at applying it to the question I have at hand. Youtube videos on the subject and even my math professor dont help.
My professor can't explain anything he says something ambiguous and follows it up with "it's easy". 
I have 3 questions 
use implicit differentiation to find $\frac{dy}{dx}$ in terms of $x$ and $y$ 
1.) $x^3-xy+y^2=4$ 
2.) $y=\sin(xy)$ 
find $\frac{d^2 y}{dx^2}$
1.) $x^2y^2 - 2x = 3$

I'll show you how to do 1), and you can try the others yourself. Differentiating implicitly, we have
$$\frac{d}{dx}(x^3 - xy + y^2) = \frac{d}{dx} 4$$
or
$$3x^2 -y -xy' + 2yy' = 0$$
so that
$$3x^2 - y = y'(x - 2y)$$
and hence
$$y' = \frac{3x^2 - y}{x - 2y}.$$
