Q. 5 What is the definition of the di... [FREE SOLUTION]

Chapter 12: Q. 5 (page 952)

What is the definition of the directional derivative for a function of two variables, $f (x, y)$ ? Be sure to include the words "unit vector" in your definition.

Short Answer

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$D_{u} f (x_{0}, y_{0}) = \lim_{h 鈫� 0} \frac{f (x_{0} + a . h, y_{0} + b . h) - f (x_{0}, y_{0})}{h}$

Step by step solution

Introduction

The given is two variables $f (x, y)$ .The objective is to find the definition of the directional derivative for a function of two variables, $f (x, y)$ . The required definitions is provided

:

Directional Derivative of a function of two variables:

Let $f (x, y)$ be a function of two variables defined on an open set containing the point $(x_{0}, y_{0})$ and let $u = (a, b)$ be a unit vector. The directional derivative of $f$ at $(x_{0}, y_{0})$ in the direction of $u$ ,denoted by $D_{u} f (x_{0}, y_{0})$ is given by,

role="math" localid="1650435210000" $D_{u} f (x_{0}, y_{0}) = \lim_{h 鈫� 0} \frac{f (x_{0} + a . h, y_{0} + b . h) - f (x_{0}, y_{0})}{h}$

Provided that limit is exists.

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91影视

What is the definition of the directional derivative for a function of two variables, $f (x, y)$ ? Be sure to include the words "unit vector" in your definition.

Short Answer

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Introduction

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91影视

What is the definition of the directional derivative for a function of two variables, f(x,y)? Be sure to include the words "unit vector" in your definition.

Short Answer

Step by step solution

Introduction

:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Discrete Mathematics

Mechanics Maths

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

What is the definition of the directional derivative for a function of two variables, $f (x, y)$ ? Be sure to include the words "unit vector" in your definition.