For the functions f(t) = e² and g(t) = e4tdefined on 0 function f(t)1tneatsin atcos atsinh atcosh ate-at f(t)U(ta) or Ua(t) (a ≥ 0)(ta) (a> 0)U(t − a)f(t − a) or Ua(t)f(t − a)f(n)(t)(−t)" f (t)-(fg)(t) = f(r)g(t − T) drLaplace transform F(s)1/s(s > 0)n!/sn+1 (s > 0)1/(s – a)(s> a)a/(s²+a²) (s > 0)s/(s² + a²)(s > 0)a/(s² - a²)(s> |a|)s/(s² – a²)F(s+a(s>|a|)-aseS S0)aseaseSF(sF(n)(s)F(s)G(s)sn¯¹ƒ (0) — sn−² ƒ'(0) … … … — ƒ (n−¹) (0)

For the functions f(t) = e² and g(t) = e 4t defined on 0 0) U(t − a)f(t − a) or Ua(t)f(t − a) f(n)(t) (−t)" f (t) - (fg)(t) = f(r)g(t − T) dr Laplace transform F(s) 1/s (s > 0) n!/sn+1 (s > 0) 1/(s – a) (s> a) a/(s²+a²) (s > 0) s/(s² + a²) (s > 0) a/(s² - a²) (s> |a|) s/(s² – a²) F(s+a (s>|a|) -as e S S 0) as e as e S F(s F(n)(s) F(s)G(s) sn ¯¹ƒ (0) — sn−² ƒ'(0) … … … — ƒ (n−¹) (0)

For the functions f(t) = e² and g(t) = e 4t defined on 0 0) U(t − a)f(t − a) or Ua(t)f(t − a) f(n)(t) (−t)" f (t) - (fg)(t) = f(r)g(t − T) dr Laplace transform F(s) 1/s (s > 0) n!/sn+1 (s > 0) 1/(s – a) (s> a) a/(s²+a²) (s > 0) s/(s² + a²) (s > 0) a/(s² - a²) (s> |a|) s/(s² – a²) F(s+a (s>|a|) -as e S S 0) as e as e S F(s F(n)(s) F(s)G(s) sn ¯¹ƒ (0) — sn−² ƒ'(0) … … … — ƒ (n−¹) (0)

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 16E

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