The derivative of a derivative

[Emethyst]

Homework Statement

Using implicit differentation, find d^2y/dx^2 (the second derivative of y with respect to x) of the following in terms of x and y: (a) xy=4 (b)4y^2-3x^2=1

Homework Equations

All the simplifying laws for derivatives

The Attempt at a Solution

I found the derivatives for both the starting equations ((a) is -y/x and (b) is 3x/4y), but I cannot seem to find the derivatives of these derivatives. I know that the answer for (a) is 2y/x^2 and the answer for (b) is 3/16y^3, but I don't know where these answers come from. The way I have tried to solve for the second derivative always ends up with a dy/dx somewhere in the solution:

ex. for (a) I wound up with (dy/dx)(-x)+y/x^2 and for (b) 12y-(12x)(dy/dx)/16y^2

If someone could be of assistance for the second part of these questions and show me where I'm going wrong it would be greatly appreciated. Thanks in advance.

 

[Dick]

Take the first one. Start with y'=(-y/x). Differentiate both sides using the quotient rule on the right. You'll get some y' terms on the right side, but you know y'=(-y/x).

 

[Emethyst]

Thanks a lot for the help, can't believe I missed that