Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

use the definition of derivative to directly prove the differentiation rules for constant and identity function

We use definition of the derivative to prove the differentiation rules for constant and identity function

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

We are given constant and identity function

Step 2: Derivative for constant function

Consider a constant function $f : R \to R$ such that $f (x) = c$ for all $x \in R$

Now we use definition of derivative

$\lim_{h \to 0} \frac{f (x + h) - f (x)}{h} \lim_{h \to 0} \frac{c - c}{h} a s f o r a n y x w e h a v e f (x) = c = 0$

Step 3: Derivative for identity function

Consider the identity function $f : R \to R$ given by $f (x) = x$

Now we apply the definition of the derivative

$\lim_{h \to 0} \frac{f (x + h) - f (x)}{h} \lim_{h \to 0} \frac{x + h - x}{h} \lim_{h \to 0} \frac{h}{h} = 1$

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Calculus

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Short Answer

use the definition of derivative to directly prove the differentiation rules for constant and identity function

Step by Step Solution

Step 1: Given information

Step 2: Derivative for constant function

Step 3: Derivative for identity function

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Calculus

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Short Answer

use the definition of derivative to directly prove the differentiation rules for constant and identity function

Step by Step Solution

Step 1: Given information

Step 2: Derivative for constant function

Step 3: Derivative for identity function

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