Dengan menggunakan konsep turunan, tentukan turunan dari fungsi-fungsi berikut. f(x)=0!1​+1!x​+2!x2​+3!x3​+⋯+n!xn​+…

Pertanyaan

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

 

  1. ... 

  2. ... 

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

turunan dari undefined adalah begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals f left parenthesis x right parenthesis end style.

Pembahasan

Pembahasan

Informasi penting: Jika suatu fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals a x to the power of n end style, maka begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals n a x to the power of n minus 1 end exponent end style

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 undefined adalah begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals f left parenthesis x right parenthesis end style.

197

5.0 (11 rating)

Muhammad Davy Bayu Anggagah

Pembahasan lengkap banget Mudah dimengerti Makasih ❤️

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