Chapter 12: Q.19 (page 953)

$U \sin g D e f i n i t i o n 12.30 a s a m o d e l, p r o v i d e a d e f i n i t i o n o f d i f f e r e n t i a b i l i t y f o r a f u n c t i o n o f n v a r i a b l e s .$

Short Answer

Expert verified

$Differentiability for a function of n variables.$ $鈭� f (P) 路 u = 0$

Step by step solution

Introduction

We have given $f (x, y) = x y + 2 x - y$ at specified point $P = (1, - 2)$ with unit vector $u = (伪, 尾) = (1, 1)$

Step 2 Directional derivative of function at point P with directional unit vector u is given by,

$鈭� f (P) 路 u = 鈭� f (1, - 2) 路 u = ({\frac{d f}{d x}|}_{(1, - 2)} i + {\frac{d f}{d y}|}_{(1, - 2)} j) 路 (\frac{i + j}{\sqrt{i^{2} + j^{2}}})$

$= [(y + 2)_{(1, - 2)} i + (x - 1)_{(1, - 2)} j] 路 (\frac{i + j}{\sqrt{2}})$

$= [(- 2 + 2) i + (1 - 1) j] 路 (\frac{i + j}{\sqrt{2}})$

$= [0 i + 0 j] 路 (\frac{i + j}{\sqrt{2}})$

$鈭� f (P) 路 u = 0$

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91影视

$U \sin g D e f i n i t i o n 12.30 a s a m o d e l, p r o v i d e a d e f i n i t i o n o f d i f f e r e n t i a b i l i t y f o r a f u n c t i o n o f n v a r i a b l e s .$

Short Answer

Step by step solution

Introduction

Step 2 Directional derivative of function at point P with directional unit vector u is given by,

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UsingDefinition12.30asamodel,provideadefinitionofdifferentiabilityforafunctionofnvariables.

Short Answer

Step by step solution

Introduction

Step 2 Directional derivative of function at point P with directional unit vector u is given by,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Discrete Mathematics

Statistics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

$U \sin g D e f i n i t i o n 12.30 a s a m o d e l, p r o v i d e a d e f i n i t i o n o f d i f f e r e n t i a b i l i t y f o r a f u n c t i o n o f n v a r i a b l e s .$