Consider f (x, y) = 7,000 - 55 x + 16 y +7 x y. Calculate partial f / partial x, partial f /...


Consider {eq}\displaystyle f (x,\ y) = 7,000 - 55 x + 16 y +7 x y {/eq}.

Calculate {eq}\displaystyle \frac {\partial f}{\partial x},\ \frac {\partial f }{\partial y},\ \frac {\partial f}{\partial x}\Bigg|_{(1, -1)}, \ \text{and}\ \frac {\partial f}{\partial y}\Bigg|_{(1,\ -1)} {/eq} when defined.

Partial Derivatives:

The first partial derivatives of a function of two variables {eq}f(x,y) {/eq} are equal to {eq}\frac {\partial f}{\partial x},\ \frac {\partial f }{\partial y} {/eq}.

Partial derivatives are calculated differentiating the function with respect to one variable while keeping

fixed the other variable.

Answer and Explanation: 1

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Given the function

{eq}\displaystyle f (x,\ y) = 7,000 - 55 x + 16 y +7 x y {/eq}

its first partial derivatives are

{eq}\displaystyle \frac...

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Learn more about this topic:

Partial Derivative: Definition, Rules & Examples


Chapter 18 / Lesson 12

What is a Partial Derivative? Learn to define first and second order partial derivatives. Learn the rules and formula for partial derivatives. See examples.

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