Partial derivative: please check work

[939]

Homework Statement

(50 - x - y)(x+y) - x - ((y^2)/2))

simplified: 50X - X^2 - XY - 50Y - XY - Y^2 - X - ((Y^2)/2)

Homework Equations

50X - X^2 - XY - 50Y - XY - Y^2 - X - ((Y^2)/2))

The Attempt at a Solution

for x:
49 - 2x - 2y

for y:
50 - 2x - 3y

The book has the same, except -1x and -1y (i.e. 49 - 1x - 2y) and (50 - 1x - 3y). Why is this?

 

[haruspex]

I agree with your answers, except you have a sign wrong in the 'simplified' equation (which gets corrected in the final answer).