Partial derivative: please check work

The correct simplified equation is 50X - X^2 - XY - 50Y - XY - Y^2 - X - ((Y^2)/2)). In summary, the simplified equation for (50 - x - y)(x+y) - x - ((y^2)/2)) is 50X - X^2 - XY - 50Y - XY - Y^2 - X - ((Y^2)/2)). The book may have a different notation for the same equation, but the end result should be the same.
  • #1
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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?
 
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  • #2
I agree with your answers, except you have a sign wrong in the 'simplified' equation (which gets corrected in the final answer).
 
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What is a partial derivative?

A partial derivative is a mathematical concept used to calculate the rate of change of a multivariable function with respect to one of its variables, while keeping all other variables constant.

What is the purpose of taking a partial derivative?

The purpose of taking a partial derivative is to understand how changes in one variable affect the overall behavior of a multivariable function. It is a useful tool in many fields of science, such as physics, engineering, and economics.

How is a partial derivative calculated?

A partial derivative is calculated by holding all other variables constant and taking the derivative of the function with respect to the variable of interest. This can be done using the same rules of differentiation as for single-variable functions.

What is the difference between a partial derivative and a total derivative?

A partial derivative only considers the changes in one variable while keeping all other variables constant, whereas a total derivative takes into account the changes in all variables at once. In other words, a total derivative is the sum of all partial derivatives.

When is it necessary to use a partial derivative?

A partial derivative is necessary when dealing with functions that have more than one independent variable. It allows us to analyze how changes in one variable affect the overall behavior of the function, and is especially useful in optimizing and solving problems in various scientific fields.

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