PERGUNTA 5 Dado ???? ∈ ℕ, considere a função ????????(????) = ???????? . Analise as derivadas ???? subscript 1 prime space left parenthesis ???? right parenthesi...

PERGUNTA 5 Dado ???? ∈ ℕ, considere a função ????????(????) = ???????? . Analise as derivadas ???? subscript 1 prime space left parenthesis ???? right parenthesis space comma space ???? subscript 2 space prime prime left parenthesis ???? right parenthesis space space comma space ???? subscript 3 space prime prime prime left parenthesis ???? right parenthesis space space e space ???? subscript 4 space prime prime prime prime left parenthesis ???? right parenthesise determine uma expressão para a derivada de ordem ???? de ????????(????), a qual é denotada por ????????(????) (????): a. f subscript n superscript left parenthesis n right parenthesis end superscript left parenthesis x right parenthesis equals n factorial b. f subscript n superscript left parenthesis n right parenthesis end superscript left parenthesis x right parenthesis equals 1 c. f subscript n superscript left parenthesis n right parenthesis end superscript left parenthesis x right parenthesis equals n x to the power of n minus 1 end exponent d. f subscript n superscript left parenthesis n right parenthesis end superscript left parenthesis x right parenthesis equals n factorial x e. f subscript n superscript left parenthesis n right parenthesis end superscript left parenthesis x right parenthesis equals n