# Partial derivative

1. Apr 17, 2007

### sapiental

1. The problem statement, all variables and given/known data

Compute dv/dx and for v = [12xy-(x^2)(y^2)]/[2(x+y)]

3. The attempt at a solution

I attemptet to solve this problem just reading over partial derivatives for the first time and get the following answer:

dv/dx (6y-xy^2)/(x+y)^2

let's say I take out the numerator and just took the partial derivative of it: i.e

(dv/dx)(12xy-(x^2)(y^2))

would the partial derivative be = 12y-2xy^2 ?

the book however gives the following answer without going through any steps because it is part of a larger problem.

dv/dx = [(y^2)(12-2xy-x^2)]/[2(x+y)^2]

I am confused because this answe is very different from mine and I can't trace my steps where I messed up.

You have the derivative of the numerator correct. The denominators derivative is just 2. Use the quotient rule. $$(\frac{u}{v})'=\frac{u'v-v'u}{v^2}$$