Explanation Given: The function is F ( x ) = ∫ x 2 cos x ( x 2 + t 2 ) 10 d t . Concept used: 1 If F ( x ) = ∫ u ( x ) v ( x ) g ( x , t ) d t then the expression of derivative from Leibniz rule is given below. F ′ ( x ) = d d x ∫ u ( x ) v ( x ) g ( x , t ) d t = g ( x , v ( x ) ) d v d x − g ( x , u ( x ) ) d u d x + ∫ u ( x ) v ( x ) ∂ ∂ x g ( x , t ) d t 2 The derivative form of Leibniz rule is given below. F ′ ( x ) = d d x ∫ u ( x ) v ( x ) g ( t ) d t = g ( v ( x ) ) d v d x − g ( u ( x ) ) d u d x . Calculation: The function is F ( x ) = ∫ x 2 cos x ( x 2 + t 2 ) 10 d t . Consider u = x 2 and v = cos x . The derivative of u and v with respect to x is calculated as follows: u = x 2 and v = cos x d u d x = 2 x and d v d x = − sin x Substitute x 2 for u ( x ) , cos x for v ( x ) and ( x 2 + t 2 ) 10

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

11th Edition

ISBN: 9781305965720

Author: Dennis G. Zill

Publisher: Cengage Learning

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Chapter A, Problem 45E

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The derivative of the function F(x)=∫x2cosx(x2+t2)10dt with the use of Leibniz’s rule.

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Chapter A Solutions

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Ch. A - In Problems 1 and 2 evaluate the given quantity....Ch. A - Prob. 2E Ch. A - Prob. 3E Ch. A - Prob. 4E Ch. A - Prob. 5E Ch. A - Prob. 6E Ch. A - Prob. 7E Ch. A - Prob. 8E Ch. A - Prob. 9E Ch. A - Prob. 10E

Ch. A - Prob. 11E Ch. A - Prob. 12E Ch. A - Prob. 13E Ch. A - Prob. 14E Ch. A - Prob. 15E Ch. A - Prob. 16E Ch. A - Prob. 17E Ch. A - Prob. 18E Ch. A - Prob. 19E Ch. A - Prob. 20E Ch. A - Prob. 21E Ch. A - Prob. 22E Ch. A - Prob. 23E Ch. A - Prob. 24E Ch. A - In Problems 25 and 26 use the indicated...Ch. A - Prob. 26E Ch. A - Prob. 27E Ch. A - Prob. 28E Ch. A - Prob. 29E Ch. A - Prob. 30E Ch. A - Prob. 31E Ch. A - Prob. 32E Ch. A - Prob. 33E Ch. A - Prob. 34E Ch. A - Show that the beta function is symmetric in x and...Ch. A - Prob. 36E Ch. A - Prob. 37E Ch. A - Prob. 38E Ch. A - Prob. 39E Ch. A - Prob. 40E Ch. A - Prob. 41E Ch. A - Prob. 42E Ch. A - Prob. 43E Ch. A - Prob. 44E Ch. A - Prob. 45E Ch. A - Prob. 46E Ch. A - Prob. 47E Ch. A - Prob. 48E Ch. A - Prob. 49E Ch. A - Prob. 50E Ch. A - Prob. 51E Ch. A - Prob. 52E Ch. A - Prob. 53E Ch. A - Prob. 54E Ch. A - Prob. 55E Ch. A - Prob. 56E

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The derivative of the function F ( x ) = ∫ x 2 cos x ( x 2 + t 2 ) 10 d t with the use of Leibniz’s rule.

Solution Summary: The author explains the derivative of the function F(x)=displaystyle int with the use of Leibniz’s rule.

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The derivative of the function F(x)=∫x2cosx(x2+t2)10dt with the use of Leibniz’s rule.

Chapter A Solutions