Given f(x, y) = 2x^3y - 3xy^3. Compute: \frac{ \partial^2 f}{\partial x^2} = \frac{...

Question:

Given {eq}f(x, y) = 2x^3y - 3xy^3. {/eq} Compute:

{eq}\frac{ \partial^2 f}{\partial x^2} = {/eq} _____

{eq}\frac{ \partial^2 f}{\partial y^2} = {/eq} _____ {eq}\pi {/eq}

Partial Derivative:

A function is of several variables, then we can easily find the partial derivative with respect to one variables. In partial derivative, we can take derivative of one variable. Treat other as constant.

Answer and Explanation:

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Given: {eq}f \left ( x, y \right ) = 2x^{3}y - 3xy^{3} {/eq}

Find the partial derivative with respect to {eq}x {/eq}.

{eq}\frac{\partial...

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Partial Derivative: Definition, Rules & Examples

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Chapter 18 / Lesson 12
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When a function depends on more than one variable, we can use the partial derivative to determine how that function changes with respect to one variable at a time. In this lesson, we use examples to define partial derivatives and to explain the rules for evaluating them.


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