THEOREM 7.4.1 Derivatives of Transforms If F(s) = {f(t)} and n = 1, 2, 3, . . . , then L{t¹f(t)} = (-1)^ d^_F(s). dsn Evaluate the given Laplace transform. (Write your answer as a function of s.) {t2 sinh t}

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 19E
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Use Theorem 7.4.1.
THEOREM 7.4.1 Derivatives of Transforms
If F(s) = L{f(t)} and n = 1, 2, 3, . . . , then
L{t^f(t)} = (−1)n dn F(s).
dsn
Evaluate the given Laplace transform. (Write your answer as a function of s.)
X{t sinh t}
Transcribed Image Text:Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, . . . , then L{t^f(t)} = (−1)n dn F(s). dsn Evaluate the given Laplace transform. (Write your answer as a function of s.) X{t sinh t}
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