Explanation Given information: Given that the function f ( x ) is differentiable that is f ' ( x ) = lim h → 0 f ( x + h ) − f ( x ) h ....... ( 1 ) Calculation: The derivative of function f 2 is given as [ f 2 ] ' ( x ) = lim h → 0 f 2 ( x + h ) − f 2 ( x ) h = lim h → 0 [ f ( x + h ) + f ( x ) ] [ f ( x + h ) − f ( x ) ] h = lim

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3.2, Problem 54PS

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To find the derivative of f2 using the definition of derivative where f is differentiable function.

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Chapter 3.2, Problem 53PS

Chapter 3.2, Problem 55PS

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Chapter 3 Solutions

Student's Solution and Survival Manual for Calculus

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To find the derivative of f 2 using the definition of derivative where f is differentiable function.

Solution Summary: The author explains how to find the derivative of f2 using the definition of derivative.

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To find the derivative of f2 using the definition of derivative where f is differentiable function.

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Chapter 3 Solutions