Chapter 12: Q. 36 (page 944)

Find the first-order partial derivatives for the functions in Exercises 27–36.
$g (x, y, z) = 2 x y + 2 x z + 2 y z$

Short Answer

Expert verified

The first-order partial derivatives are $\frac{\partial g}{\partial x} = 2 y + 2 z, \frac{\partial g}{\partial y} = 2 x + 2 z, \frac{\partial g}{\partial z} = 2 x + 2 y .$

Step by step solution

Given

The given function is: $g (x, y, z) = 2 x y + 2 x z + 2 y z$

To find

We have to find the first-order partial derivatives.

Calculation

$g (x, y, z) = 2 x y + 2 x z + 2 y z \frac{\partial g}{\partial x} = \frac{\partial}{\partial x} (2 x y + 2 x z + 2 y z) \frac{\partial g}{\partial x} = 2 y + 2 z g (x, y, z) = 2 x y + 2 x z + 2 y z \frac{\partial g}{\partial y} = \frac{\partial}{\partial y} (2 x y + 2 x z + 2 y z) \frac{\partial g}{\partial y} = 2 x + 2 z g (x, y, z) = 2 x y + 2 x z + 2 y z \frac{\partial g}{\partial z} = \frac{\partial}{\partial z} (2 x y + 2 x z + 2 y z) \frac{\partial g}{\partial z} = 2 x + 2 y Hence, \frac{\partial g}{\partial x} = 2 y + 2 z, \frac{\partial g}{\partial y} = 2 x + 2 z, \frac{\partial g}{\partial z} = 2 x + 2 y .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the first-order partial derivatives for the functions in Exercises 27–36.
$g (x, y, z) = 2 x y + 2 x z + 2 y z$

Short Answer

Step by step solution

Given

To find

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Logic and Functions

Statistics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the first-order partial derivatives for the functions in Exercises 27–36. gx,y,z=2xy+2xz+2yz

Short Answer

Step by step solution

Given

To find

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Logic and Functions

Statistics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the first-order partial derivatives for the functions in Exercises 27–36.
$g (x, y, z) = 2 x y + 2 x z + 2 y z$