Find {eq}\displaystyle \frac{\partial z}{\partial y} \ {/eq} if {eq}\ xyz = cos(2x + 3y -z) {/eq}.


Find {eq}\displaystyle \frac{\partial z}{\partial y} \ {/eq} if {eq}\ xyz = cos(2x + 3y -z) {/eq}.

Partial Derivatives:

When taking a partial derivative with respect to, {eq}x {/eq}, you treat the variable {eq}y {/eq} as if it is a constant. When we take the partial derivative with respect to, for example, {eq}x {/eq}, we take all other variables as constant for that particular instant. Partial derivatives are used in a variety of applications, including Lagrange multipliers, absolute maxima and minima, gradient vectors, tangent and normal lines, and many others.

Answer and Explanation: 1

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Given {eq}\displaystyle xyz = \cos(2x + 3y -z) {/eq}

Partially differentiating {eq}\displaystyle z {/eq} with respect to {eq}\displaystyle ...

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Partial Derivative: Definition, Rules & Examples


Chapter 18 / Lesson 12

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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