Consider the following multivariate function: Y = 6X_1 X_2^(1/2) i) Find the partial derivative...

Question:

Consider the following multivariate function:

{eq}Y = 6X_{1} X_{2}^{\frac{1}{2}} {/eq}

i) Find the partial derivative of Y with respect to {eq}X_{1} {/eq}

ii) Find the partial derivative of Y with respect to {eq}X_{2} {/eq}

Partial Derivatives:

The partial derivative of a function of several variables is the derivative of the respective variable holding all other variables as constant. The regular rules of differential apply when taking partial derivatives. Partial derivatives are often used in optimization problems where functions depend on several variables.

Answer and Explanation: 1

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i) Find the partial derivative of Y with respect to {eq}X_{1} {/eq}

We can compute the partial derivative by using the power-rule of...

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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 to define first and second order partial derivatives. Learn the rules and formula for partial derivatives. See examples.


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