Consider f (x, y) = 7,000 - 55 x + 16 y +7 x y. Calculate partial f / partial x, partial f /...
Question:
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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View this answerGiven 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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Partial Derivative | Definition, Rules & Examples
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Chapter 18 / Lesson 12
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What is a Partial Derivative? Learn what symbol is used for partial derivatives. Learn to define first and second order partial derivatives. Learn the rules and formula for partial derivatives. Work through partial derivative examples with solutions.
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