- #1
manenbu
- 103
- 0
Homework Statement
Assume that the following equation define the implicit function y=(x). Find the its derivative:
x2 + 2xy - y2 = a2
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 = x2 + 2xy - y2 - a2 = 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 2a2 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.