Answer to Question #251955 in Calculus for JaytheCreator

Question

Let 𝐹(𝑠) = ℒ{𝑓(𝑡)}. Prove that

ℒ { 𝑑^𝑛𝑓(𝑡)/ 𝑑𝑡^𝑛 } = 𝑠^𝑛𝐹(𝑠) − 𝑠^𝑛−1𝑓(0) − ⋯ − 𝑑^𝑛−1𝑓(0) /𝑑𝑡^𝑛−1

Hint: Try induction