# Find the value of (partial x)/(partial z) at the point (1, -1, -3) if the equation xz + y*ln x -...

## Question:

Find the value of {eq}\frac{\partial x}{\partial z} {/eq} at the point {eq}(1, -1, -3) {/eq} if the equation {eq}xz + y \ln x - x^2 + 4 = 0 {/eq} defines {eq}x {/eq} as a function of the two independent variables {eq}y {/eq} and {eq}z {/eq} and the partial derivative exists.

## Basic Meaning of Partial Derivatives:

We discuss two kinds of derivatives in calculus: partial and ordinary derivatives. The partial derivatives {eq}\dfrac{\partial f}{\partial x} {/eq} refer to the rate of change of {eq}f(x,y) {/eq} when we change the variable {eq}x {/eq} while there is no variation in {eq}y {/eq}. In addition, the derivative {eq}\dfrac{\partial f}{\partial y} {/eq} is the rate of change of {eq}f(x,y) {/eq} when we change the variable {eq}y {/eq} while there is no variation in {eq}x {/eq}.

## Answer and Explanation: 1

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View this answerConsider the implicit equation {eq}xz+y \ln x-x^2+4=0 {/eq}.

We know that {eq}x {/eq} is a function of two independent variables {eq}y {/eq} and...

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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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