Partial Derivatives....help!

**leungsta** · October 9th 2008, 02:19 PM

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

**Jhevon** · October 9th 2008, 02:30 PM

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, $\frac {\partial^2 v}{\partial x^2} = \frac {\partial}{\partial x} \left( \frac {\partial v}{\partial x} \right) = 2y^2(x - y)^{-3}$

**Chris L T521** · October 9th 2008, 02:30 PM

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

**leungsta** · October 9th 2008, 02:44 PM

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

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