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## Homework Statement

Find the second partial derivatives.

z= x/(x+y)

## The Attempt at a Solution

I solved the correct df/dx, d^2f/dx^2, df/dy, and d^2f/dy^2, however I can't seem to get the correct answer for d^2f/dydx and d^2f/dxdy.

My df/dx is y/(x+y)^2 which I changed to y((x+y)^-2)

Differentiating with respect to y, using the product rule: (1)(x+y)^-2 + y(-2)((x+y)^-3) = (x+y)^-2 - 2y((x+y)^-3)

My df/dy is -x((x+y)^-2)

Differentiating with respect to x, using the product rule: (-1)(x+y)^-2 + (-x)(-2)((x+y)^-3) = -(x+y)^-2 + 2x((x+y)^-3)

I know they aren't right b/c 1) they don't equal each other (Clairaut's Thm.) and 2) it doesn't match the book's answer =)

Can anyone catch the mistake I'm making? Thank you.

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