Partial derivative Compute dv/dx

[sapiental]

Homework Statement

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

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.

Please help!

 

[Gib Z]

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

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