Explanation Given Information: The provided function is y = ( 5 x 6 + 6 x 4 + 5 ) 6 . Formula used: Power rule for a real number n is such that, if y = u n then d y d x = n u n − 1 ⋅ d u d x , where u is a differentiable function of x . Power of x rule for function f ( x ) = x n is f ′ ( x ) = n x n − 1 , where n is a real number. Coefficient rule for a constant c is such that, if f ( x ) = c ⋅ u ( x ) , where u ( x ) is a differentiable function of x , then f ′ ( x ) = c ⋅ u ′ ( x ) . Constant function rule for a constant c is such that, if f ( x ) = c then f ′ ( x ) = 0 . Calculation: Consider the function, y = ( 5 x 6 + 6 x 4 + 5 ) 6 Consider ( 5 x 6 + 6 x 4 + 5 ) to be u , y = u 6 Differentiate both sides with respect to x , y ′ = d d x ( u 6 ) Use the power of x rule, y ′ = 6 ⋅ u 6 − 1 ⋅ d u d x = 6 u 5 d u d x Substitute ( 5 x 6 + 6 x 4 + 5 ) for u , y ′ = 6 ( 5 x 6 + 6

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Differential Equations

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Chapter 9, Problem 70RE

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To calculate: The value of y′ for the function y=(5x6+6x4+5)6.

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Chapter 9, Problem 69RE

Chapter 9, Problem 71RE

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Chapter 9 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 9.1 - 1. Can exist if is undefined? Ch. 9.1 - 2. Does exist if ? Ch. 9.1 - 3. Does Ch. 9.1 - 4. If , does exist? Ch. 9.1 - 5. Let (a) Does (b) Find . Ch. 9.1 - 6. Evaluate the following limits (if they...Ch. 9.1 - Prob. 7CP Ch. 9.1 - Prob. 8CP Ch. 9.1 - Prob. 9CP Ch. 9.1 - Prob. 10CP

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The value of y ′ for the function y = ( 5 x 6 + 6 x 4 + 5 ) 6 .

Solution Summary: The author calculates the value of yprime for the function, which is 6(30x5+24

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To calculate: The value of y′ for the function y=(5x6+6x4+5)6.

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Chapter 9 Solutions