Q. 36 Find the first-order partial der... [FREE SOLUTION]

Chapter 12: Q. 36 (page 944)

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

Short Answer

Expert verified

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

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

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

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91影视

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

Short Answer

Step by step solution

Given

To find

Calculation

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91影视

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

Short Answer

Step by step solution

Given

To find

Calculation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Decision Maths

Discrete Mathematics

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

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