# Let f(x, y, z) = x^2 y^3 z^4. Find partial differential^3 f / partial differential z partial...

## Question:

Let {eq}f(x, y, z) = x^2 y^3 z^4. {/eq} Find {eq}\frac{\partial^3 f}{\partial z \partial y \partial x} (4, 3, 2). {/eq} REMINDER {eq}\frac{\partial^3 f}{\partial z \partial y \partial x} = \frac{\partial}{\partial z } (\frac{\partial}{\partial z}(\frac{\partial f}{\partial x})). {/eq}

## Partial Derivatives

First differentiate the given function partially with respect to x, where y, z acts as constant. Then differentiate the given function partially with respect to y, where x, z acts as constant. Now differentiate the given function partially with respect to z, where y, x acts as constant. Then substitute the given point.

{eq}\displaystyle \frac{\partial x^n}{\partial x}=nx^{n-1}{/eq}

## Answer and Explanation: 1

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{eq}\displaystyle f(x, y, z) = x^2 y^3 z^4{/eq}

Now differentiating f(x,y,z) partially with respect to x, where y, z remains constant.

{eq}\d...

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Chapter 18 / Lesson 12What 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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