1. ## Partial Derivatives....help!

Calculate all second derivatives for v = xy/(x-y)

2. Originally Posted by leungsta
Calculate all second derivatives for v = xy/(x-y)
i will do $\frac {\partial v}{\partial x}$ and $\frac {\partial^2 v}{\partial x^2}$, the partial derivatives with respect to $y$ are similar.

when taking the partial derivatives with respect to $x$, you treat all other variables as constants. so my $y$'s might as well be 2's now

thus, by the quotient rule: $\frac {\partial v}{\partial x} = \frac {(x - y)y - xy}{(x - y)^2} = \frac {-y^2}{(x - y)^2} = -y^2 (x - y)^{-2}$

thus, by the chain rule, $\frac {\partial^2 v}{\partial x^2} = \frac {\partial}{\partial x} \left( \frac {\partial v}{\partial x} \right) = 2y^2(x - y)^{-3}$

3. Originally Posted by leungsta
Calculate all second derivatives for v = xy/(x-y)
Did you first compute $\frac{\partial v}{\partial x}$, $\frac{\partial v}{\partial y}$??

--Chris

4. Originally Posted by Chris L T521
Did you first compute $\frac{\partial v}{\partial x}$, $\frac{\partial v}{\partial y}$??

--Chris
Nope I tried doing the first partial derivative but wasn't sure how to do it