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Given {eq}\displaystyle {/eq}, find {eq}\displaystyle \frac {\partial^{6}u}{\partial x \; \partial y^{2} \; \partial z^{3}}{/eq}.

Question:

Given {eq}\displaystyle {/eq}, find {eq}\displaystyle \frac {\partial^{6}u}{\partial x \; \partial y^{2} \; \partial z^{3}}{/eq}.

PARTIAL DIFFERENTIATION

Given a function of two variables {eq}{\rm{f(x,y)}} {/eq} The derivative with respect to x only treating y as constant only is called partial derivative of f with respect to x and is denoted by

{eq}\frac{{\partial f}}{{\partial x}} {/eq}

Answer and Explanation: 1

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{eq}\begin{array}{l} u = {x^a}{y^b}{z^c};\\ \frac{{{\partial ^6}u}}{{\partial x\partial {y^2}\partial {z^3}}}\\ \frac{{\partial u}}{{\partial x}} =...

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The Chain Rule for Partial Derivatives

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Chapter 14 / Lesson 4
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This lesson defines the chain rule. It goes on to explore the chain rule with partial derivatives and integrals of partial derivatives.


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