Hi All!

Having a problem when differentiating for the second time $\displaystyle \frac{d^2y}{dx^2}$an implicit equation.

I'll give two example problems:

$\displaystyle 2x^2 + 2y^2 - 4x + 6 = 0}$

$\displaystyle = 4x + 4y.\frac{dy}{dx} -4 = 0$

$\displaystyle \frac{dy}{dx} = \frac{4 - 4x}{4y}$

Not to sure how to take it from here to do the second derivative $\displaystyle (\frac{d^2y}{dx^2})$

Second problem:

$\displaystyle y^2 + x^2 = 1 $

$\displaystyle 2y.\frac{dy}{dx} + 2x = 0 $

$\displaystyle \frac{dy}{dx} = -\frac{2x}{2y}$

Also not sure how to take it from here to get $\displaystyle \frac{d^2y}{dx^2}$.

Your help will be appreciated. Thanks

Regards,

dadon