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Transformada de laplace primera derivada

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transformada con derivadas

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Transformada de laplace primera derivada

  1. 1. Transformadas de Derivadas
  2. 2. 𝐿 𝑓´ 𝑑 = 0 π‘’βˆ’π‘ π‘‘ 𝑓´ 𝑑 𝑑𝑑 𝑒 = π‘’βˆ’π‘ π‘‘ 𝑑𝑒 = βˆ’π‘ π‘’βˆ’π‘ π‘‘ 𝑑𝑑 𝑑𝑣 = 𝑓´ 𝑑 𝑑𝑑 𝑣 = 𝑓´ 𝑑 𝑑𝑑 𝑣 = 𝑓 𝑑 𝑒 βˆ™ 𝑑𝑣 = 𝑒 βˆ™ 𝑣 βˆ’ 𝑣 βˆ™ 𝑑𝑒 𝑒 𝑑𝑣
  3. 3. = π‘’βˆ’π‘ π‘‘ βˆ™ 𝑓(𝑑) ∞ 0 + 𝑠 0 ∞ π‘’βˆ’π‘ π‘‘ 𝑓 𝑑 𝑑𝑑 = lim π‘β†’βˆž π‘’βˆ’π‘ (𝑏) βˆ™ 𝑓 βˆ’ 𝑏 βˆ’ π‘’βˆ’π‘  0 βˆ™ 𝑓 0 + 𝑠𝐿 𝑓(𝑑) = lim 𝑏 β†’ ∞ 𝑓(𝑏) π‘’βˆ’π‘ (𝑏) βˆ’ 1 βˆ™ 𝑓 0 + 𝑠𝐿 𝑓(𝑑) = βˆ’π‘“ 0 + 𝑠 𝐿 𝑓(𝑑) = βˆ’π‘“ 0 + 𝑠 𝐹 𝑠 𝐿 𝑓(𝑑) = 𝑠 𝐹 𝑠 βˆ’ 𝑓(0)

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