While doing implicit differentiation I am asked to take a 2nd derivative of $$x^2+3y^2 = 9$$
The first derivative: $$\frac{dy}{dx} = \frac{-x}{3y}$$
Now the second derivative with the quotient rule I stopped here: $$\frac{-3y+3x\frac{dy}{dx}}{9y^2}$$
From here I need to isolate the $3x\frac{dy}{dx}$ and then solve for $\frac{dy}{dx}$. How do I get the $3x\frac{dy}{dx}$ out of the numerator?
You should write a full equation $$\frac {d^2y}{dx^2}=\frac{-3y+3x\frac{dy}{dx}}{9y^2}.$$ You have a value for $\frac {dy}{dx}$, so substitute it in and you are done.