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

Expert verified

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

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

Provided that limit is exists.

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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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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

Discrete Mathematics

Applied Mathematics

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Decision Maths

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.