# Math Help - Help w/ implicit differentiation

1. ## Help w/ implicit differentiation

I don't really get this method, it wasn't explained thoroughly in the book. It says:
"Differentiate term by term through the function, remembering that in differentiating functions of y you are differentiating a function of a function".

Then it gives an example:

Find $\frac{dy}{dx}$ of $x^2-y^2 +3x = 5y$
$2x-2y\frac{dy}{dx}+3=5\frac{dy}{dx}$
$\frac{dy}{dx}=\frac{2x+3}{2y+5}$

I don't know why $\frac{d}{dx}(y^2)=2y\frac{dy}{dx}$. I know that y is really a polynomial in x and that 'somehow' complicates things, but it doesn't make sense to me to just add a $\frac{dy}{dx}$ to the end
I also never knew you could differentiate an 'equation'... could you effectively write this $\frac{d}{dx}($Equation $)$?

2. When you have $\frac{dy}{dx}$ you know you're differentiating respect to $x$, and when you take the derivative of $y$, you use the chain rule, for that reason yields $\frac{dy}{dx}~y^2=2yy'$