Explanation Given Information: The provided function is y = ( 2 x − 1 x 2 + x ) 4 . 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 . Quotient rule for function f ( x ) = u ( x ) v ( x ) , where u and v are differentiable functions of x , then f ′ ( x ) = v ( x ) ⋅ u ′ ( x ) − u ( x ) ⋅ v ′ ( x ) [ v ( x ) ] 2 . 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 = ( 2 x − 1 x 2 + x ) 4 Consider 2 x − 1 x 2 + x to be u , y = u 4 Differentiate both sides with respect to x , d y d x = d d x ( u 4 ) Use the power rule, y ′ = 4 ⋅ u 4 − 1 ⋅ d u d x = 4 u 3 d u d x Substitute 2 x − 1 x 2 + x for u , y ′ = 4 ( 2 x − 1 x 2 + x ) 3 d d x ( 2 x − 1 x 2 + x )

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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Chapter 9.7, Problem 23E

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To calculate: The simplified form of the derivative of the function y=(2x−1x2+x)4.

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Chapter 9.7, Problem 22E

Chapter 9.7, Problem 24E

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Using FDF, BDF, and CDF, find the first derivative; 1. The distance x of a runner from a fixed point is measured (in meters) at an interval of half a second. The data obtained is: t 0 x 0 0.5 3.65 1.0 1.5 2.0 6.80 9.90 12.15 Use CDF to approximate the runner's velocity at times t = 0.5s and t = 1.5s 2. Using FDF, BDF, and CDF, find the first derivative of f(x)=x Inx for an input of 2 assuming a step size of 1. Calculate using Analytical Solution and Absolute Relative Error: = True Value - Approximate Value| x100 True Value 3. Given the data below where f(x) sin (3x), estimate f(1.5) using Langrage Interpolation. x 1 1.3 1.6 1.9 2.2 f(x) 0.14 -0.69 -0.99 -0.55 0.31 4. The vertical distance covered by a rocket from t=8 to t=30 seconds is given by: 30 x = Loo (2000ln 140000 140000 - 2100 9.8t) dt Using the Trapezoidal Rule, n=2, find the distance covered. 5. Use Simpson's 1/3 and 3/8 Rule to approximate for sin x dx. Compare the results for n=4 and n=8

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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 simplified form of the derivative of the function y = ( 2 x − 1 x 2 + x ) 4 .

Solution Summary: The author explains the simplified form of the derivative of y=(2x-1x 2+x

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To calculate: The simplified form of the derivative of the function y=(2x−1x2+x)4.

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Chapter 9 Solutions