Pertanyaan

Dengan menggunakan konsep turunan, tentukan turunan dari fungsi-fungsi berikut. f ( x ) = 0 ! 1 + 1 ! x + 2 ! x 2 + 3 ! x 3 + ⋯ + n ! x n + …

Dengan menggunakan konsep turunan, tentukan turunan dari fungsi-fungsi berikut.

$f (x) = \frac{1}{0 !} + \frac{x}{1 !} + \frac{x ^{2}}{2 !} + \frac{x ^{3}}{3 !} + \dots + \frac{x ^{n}}{n !} + \dots$

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Informasi penting: Jika suatu fungsi , maka Maka turunannya Jadi turunan dari adalah .

Informasi penting: Jika suatu fungsi , maka

Maka turunannya

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator 0 factorial end fraction plus fraction numerator x over denominator 1 factorial end fraction plus fraction numerator x squared over denominator 2 factorial end fraction plus fraction numerator x cubed over denominator 3 factorial end fraction plus horizontal ellipsis plus fraction numerator x to the power of n over denominator n factorial end fraction plus horizontal ellipsis end cell row cell f to the power of apostrophe left parenthesis x right parenthesis end cell equals cell 0 plus 1 plus fraction numerator 2 x over denominator 2 end fraction plus fraction numerator 3 x squared over denominator 6 end fraction plus fraction numerator 4 x cubed over denominator 24 end fraction plus horizontal ellipsis plus fraction numerator n x to the power of n minus 1 end exponent over denominator n factorial end fraction plus horizontal ellipsis end cell row blank equals cell 1 plus x plus x squared over 2 plus x cubed over 6 plus horizontal ellipsis plus fraction numerator x to the power of n minus 1 end exponent over denominator open parentheses n minus 1 close parentheses factorial end fraction plus horizontal ellipsis end cell row blank equals cell fraction numerator 1 over denominator 0 factorial end fraction plus fraction numerator x over denominator 1 factorial end fraction plus fraction numerator x squared over denominator 2 factorial end fraction plus fraction numerator x cubed over denominator 3 factorial end fraction plus horizontal ellipsis plus fraction numerator x to the power of n minus 1 end exponent over denominator open parentheses n minus 1 close parentheses factorial end fraction plus fraction numerator x to the power of n over denominator n factorial end fraction plus horizontal ellipsis end cell row blank equals cell f left parenthesis x right parenthesis end cell end table end style$

Jadi turunan dari adalah .