Explanation The derivative of the function is basically the method to determine the rate of change of one value with respect to some other variable. The n t h derivative is determined by deriving the function n times and can be represented as f ( n ) ( x ) = [ f ( n − 1 ) ( x ) ] ′ For example, Consider a function, f ( x ) = e x Fourth derivative of the function with respect to x is, f ( 4 ) ( x ) = [ e x ] ′ ′ ′ ′ Solve the above function as, f ( 4 ) ( x ) = [ e x ] ′ ′ ′ = [ e x ] ′ ′ = [ e x ] ′ = e x Consider another example, f ( x ) = e − x Fourth derivative of the function with respect to x is, f ( 4 ) ( x ) = [ e − x ] ′ ′ ′ ′ Solve the above function as, f ( 4 ) ( x ) = [ − e − x ] ′ ′ ′ = [ e − x ] ′ ′ = [ − e − x ] ′

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Chapter 16.2, Problem 78E

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The four examples of a function f(x) with the property that f(4)(x)=f(x).

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Chapter 16.2, Problem 77E

Chapter 16.2, Problem 79E

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Chapter 16 Solutions

EBK FINITE MATH AND APPLIED CALCULUS

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

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The four examples of a function f ( x ) with the property that f ( 4 ) ( x ) = f ( x ) .

Solution Summary: The author explains that the derivative of the function is basically the method to determine the rate of change of one value with respect to another variable.

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The four examples of a function f(x) with the property that f(4)(x)=f(x).

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Chapter 16 Solutions