Answer to Question #251955 in Calculus for JaytheCreator

Question #251955

Let 𝐹(𝑠) = β„’{𝑓(𝑑)}. Prove that

β„’ { 𝑑^𝑛𝑓(𝑑)/ 𝑑𝑑^𝑛 } = 𝑠^𝑛𝐹(𝑠) βˆ’ 𝑠^π‘›βˆ’1𝑓(0) βˆ’ β‹― βˆ’ 𝑑^π‘›βˆ’1𝑓(0) /𝑑𝑑^π‘›βˆ’1

Hint: Try inductionΒ 


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