Consider f (x, y, z) = x / {y - z}. Compute the partial derivative below. {partial f} / {partial...


Consider {eq}\displaystyle f (x,\ y,\ z) = \dfrac x {y - z} {/eq}. Compute the partial derivative below.

{eq}\displaystyle \dfrac {\partial f} {\partial x}_{(2,\ -1,\ 3)} {/eq}.

Partial Differentiation

While partially differentiating the function {eq}\displaystyle f(x,y,z) {/eq} with respect to {eq}\displaystyle x {/eq}, the variables {eq}\displaystyle y,z {/eq} are considered as constants.

Simply it can be stated that while partially differentiating a function with respect to a particular variable, others are considered as constants.

We need to know that {eq}\displaystyle \frac{d}{dx} x^n = nx^{n-1},\frac{d}{dx} k=0 {/eq} where {eq}\displaystyle k {/eq} is a constant.

Answer and Explanation: 1

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We have,

{eq}\displaystyle f (x,\ y,\ z) = \dfrac x {y - z} {/eq}.

Let us apply the partial differentiation with respect to x we get,


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Learn more about this topic:

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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