Explanation Given: The following functions a) f ( x ) = cot ( x 2 ) b) f ( x ) = x 3 + 1 Key concepts applied: A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. Computer algebra systems can represent parameters and variables in equations as symbols. Using a CAS we can solve, manipulate, and plot a function without having to generate numeric data. Let us use MATLAB to do the given calculations. In MATLAB, to perform differentiation , First, represent the given function f by using the command “syms” to create the symbolic function f(x) and then represent differentiation using the “diff” function. MATLAB lends itself to solve more complex differential equations as well. Calculation: a) f ( x ) = cot ( x 2 ) Description MATLAB CODE Result Step 1. Represent the given function f syms x f ( x ) = cot ( x 2 ) Step 2. represent differentiation for f k ( x ) k = 1 f1=diff(f) f 1 = − 2 x ( csc 2 ( x 2 ) ) Step 3. represent differentiation for f k ( x ) k = 2 f2=diff(f1) f 2 = 2 csc 2 ( x 2 ) ( 4 x 2 cot ( x 2 ) − 1 ) Step 4

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Chapter 3.7, Problem 96E

To determine

To calculate:

The first second and third derivatives of the given functions using a computer algebra system

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Chapter 3.7, Problem 95E

Chapter 3.7, Problem 97E

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Chapter 3 Solutions

Calculus - Standalone book

Ch. 3.1 - Prob. 1PQ Ch. 3.1 - Prob. 2PQ Ch. 3.1 - Prob. 3PQ Ch. 3.1 - Prob. 4PQ Ch. 3.1 - Prob. 5PQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E

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The first second and third derivatives of the given functions using a computer algebra system

Solution Summary: The author calculates the first second and third derivatives of the given functions using a computer algebra system in MATLAB.

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The first second and third derivatives of the given functions using a computer algebra system