- #1

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## Homework Statement

Assume that the following equation define the implicit function y=(x). Find the its derivative:

x

^{2}+ 2xy - y

^{2}= a

^{2}

y

^{'}=?

y

^{''}=?

## Homework Equations

[tex]\frac{dy}{dx} = -\frac{F_x}{F_y}[/tex]

## The Attempt at a Solution

so for the first derivative I express that equation as F = x

^{2}+ 2xy - y

^{2}- a

^{2}= 0 and using the rule from above I get:

[tex]y^{'} = -\frac{x+y}{x-y}[/tex] which is correct.

For the second derivative the answer should be:

[tex]y^{''} = \frac{2a^{2}}{(x-y)^{3}}[/tex]

But I don't understand how to get there. Where did the 2a

^{2}come from? the

^{3}hints to me that I need to make a derivative of the fraction, but I can't seem to get anything useful.