Explanation Given: The function is f ( x ) = 1 5 x 5 + ( x 2 + 1 ) ( x 2 − x − 1 ) + 28 . Formula used : The product rule of differentiation is, f ' ( x ) = d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) Calculation: Solve the given function to get the derivative of function. f ' ( x ) = d d x [ 1 5 x 5 + ( x 2 + 1 ) ( x 2 − x − 1 ) + 28 ] f ' ( x ) = 1 5 ⋅ 5 x 4 + d d x [ ( x 2 + 1 ) ( x 2 − x − 1 ) ] + 0 f ' ( x ) = x 4 + d d x [ ( x 2 + 1 ) ( x 2 − x − 1 ) ] Use the product rule in the second term of above function

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 3.2, Problem 10E

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To find: The derivative of given function.

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According to Newton's law of universal gravitation, the force F between two bodies of constant mass GmM m and M is given by the formula F = , where G is the gravitational constant and d is the d² distance between the bodies. a. Suppose that G, m, and M are constants. Find the rate of change of force F with respect to distance d. F' (d) 2GmM b. Find the rate of change of force F with gravitational constant G = 6.67 × 10-¹¹ Nm²/kg², on two bodies 5 meters apart, each with a mass of 250 kilograms. Answer in scientific notation, rounding to 2 decimal places. -6.67x10 N/m syntax incomplete.

Chapter 3 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

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The derivative of given function.

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Chapter 3 Solutions