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Jika begin mathsize 14px style f open parentheses x minus 1 close parentheses equals 4 x squared minus 2 x end style, maka begin mathsize 14px style f apostrophe open parentheses 2 close parentheses equals.... end style 

Pembahasan Video:

Pembahasan Soal:

Diketahui begin mathsize 14px style f open parentheses x minus 1 close parentheses equals 4 x squared minus 2 x end style, dimisalkan begin mathsize 14px style x minus 1 equals a space space space space space x equals a plus 1 end style maka:

begin mathsize 14px style f open parentheses x minus 1 close parentheses equals 4 x squared minus 2 x space space space space space space f open parentheses a close parentheses equals 4 open parentheses a plus 1 close parentheses squared minus 2 open parentheses a plus 1 close parentheses space space space space space space f open parentheses a close parentheses equals 4 open parentheses a squared plus 2 a plus 1 close parentheses minus 2 a minus 2 space space space space space space f open parentheses a close parentheses equals 4 a squared plus 8 a plus 4 minus 2 a minus 2 space space space space space space f open parentheses a close parentheses equals 4 a squared plus 6 a plus 2 space space space space space space f open parentheses x close parentheses equals 4 x squared plus 6 x plus 2 end style  

Sehingga:

begin mathsize 14px style f open parentheses x close parentheses equals 4 x squared plus 6 x plus 2 f apostrophe open parentheses x close parentheses equals 8 x plus 6 f apostrophe open parentheses 2 close parentheses equals 8 open parentheses 2 close parentheses plus 6 f apostrophe open parentheses 2 close parentheses equals 16 plus 6 f apostrophe open parentheses 2 close parentheses equals 22 end style 

Jadi, nilai  begin mathsize 14px style f apostrophe open parentheses 2 close parentheses end style adalah begin mathsize 14px style 22 end style.

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Dijawab oleh:

D. Entry

Terakhir diupdate 07 Juni 2021

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Pertanyaan yang serupa

Turunan fungsi adalah

Pembahasan Soal:

Ingat :

rightwards arrow 1 over x to the power of n equals x to the power of negative n end exponent rightwards arrow f left parenthesis x right parenthesis equals a x to the power of n rightwards arrow f apostrophe left parenthesis x right parenthesis equals a n x to the power of n minus 1 end exponent

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 2 over denominator 3 x to the power of begin display style bevelled 2 over 3 end style end exponent end fraction minus 3 over x to the power of begin display style bevelled 5 over 2 end style end exponent plus fraction numerator 1 over denominator 4 x to the power of begin display style bevelled 3 over 2 end style end exponent end fraction end cell row blank equals cell 2 over 3 x to the power of negative bevelled 2 over 3 end exponent minus 3 x to the power of negative bevelled 5 over 2 end exponent plus 1 fourth x to the power of negative bevelled 3 over 2 end exponent end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell negative 4 over 9 x to the power of negative bevelled 5 over 3 end exponent plus 15 over 2 x to the power of negative bevelled 7 over 2 end exponent minus 3 over 8 x to the power of negative bevelled 5 over 2 end exponent end cell row blank equals cell negative fraction numerator 4 over denominator 9 x to the power of begin display style bevelled 5 over 3 end style end exponent end fraction plus fraction numerator 15 over denominator 2 x to the power of begin display style bevelled 7 over 2 end style end exponent end fraction minus fraction numerator 3 over denominator 8 x to the power of begin display style bevelled 5 over 2 end style end exponent end fraction end cell end table  

Jadi, jawaban yang teapt adalah A.

1

Roboguru

Diketahui . Turunan pertama dari f(x) adalah f'(x)=.....

Pembahasan Soal:

straight f left parenthesis straight x right parenthesis equals 2 straight x cubed minus 2 straight x squared minus 4 straight x plus 1  straight f to the power of apostrophe left parenthesis straight x right parenthesis equals 2.3 straight x to the power of 3 minus 1 end exponent minus 2.2 straight x to the power of 2 minus 1 end exponent minus 4.1 straight x to the power of 1 minus 1 end exponent  straight f to the power of apostrophe left parenthesis straight x right parenthesis equals 6 straight x squared minus 4 straight x minus 4

0

Roboguru

Tentukan fungsi  dalam  untuk setiap bentuk berikut.

Pembahasan Soal:

Diketahui fungsi:

begin mathsize 14px style fraction numerator d y over denominator d x end fraction equals 2 over 3 x cubed plus 1 half x squared plus 1 third x plus 1 over 6 end style

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d y over denominator d x end fraction end cell equals cell 2 over 3 x cubed plus 1 half x squared plus 1 third x plus 1 over 6 end cell row cell y apostrophe end cell equals cell fraction numerator 2 over denominator up diagonal strike 3 end fraction times up diagonal strike 3 times x to the power of 3 minus 1 end exponent plus fraction numerator 1 over denominator up diagonal strike 2 end fraction times up diagonal strike 2 times x to the power of 2 minus 1 end exponent plus 1 third times 1 times x to the power of 1 minus 1 end exponent plus 0 end cell row cell y apostrophe end cell equals cell 2 x squared plus x plus 1 third end cell end table 

Jadi, fungsi begin mathsize 14px style y end style dalam size 14px x untuk fungsi begin mathsize 14px style fraction numerator d y over denominator d x end fraction equals 2 over 3 x cubed plus 1 half x squared plus 1 third x plus 1 over 6 end style adalah y apostrophe equals 2 x squared plus x plus 1 third.

0

Roboguru

Diketahui  maka ...

Pembahasan Soal:

Dengan menggunakan konsep turunan pada fungsi aljabar maka diperoleh turunan dari begin mathsize 14px style f open parentheses x close parentheses equals 4 x cubed minus 3 x squared plus 2 x minus 1 end style:

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 4 x cubed minus 3 x squared plus 2 x minus 1 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 4 times 3 space x to the power of 3 minus 1 end exponent minus 3 times 2 space x to the power of 2 minus 1 end exponent plus 2 times 1 x to the power of 1 minus 1 end exponent end cell row blank equals cell 12 x squared minus 6 x plus 2 end cell end table end style 

Oleh karena itu, jawaban yang benar adalah C.

0

Roboguru

Tentukan turunan dari fungsi-fungsi berikut ini:

Pembahasan Soal:

Gunakan konsep turunan fungsi aljabar:

table row cell f open parentheses x close parentheses equals a x to the power of n end cell rightwards arrow cell f apostrophe open parentheses x close parentheses equals a times n x to the power of n minus 1 end exponent end cell row cell f open parentheses x close parentheses equals a end cell rightwards arrow cell f apostrophe open parentheses x close parentheses equals 0 end cell end table

sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 11 plus 2 square root of x minus 5 x end cell row cell f open parentheses x close parentheses end cell equals cell 11 plus 2 x to the power of 1 half end exponent minus 5 x end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 0 plus 2 times 1 half x to the power of 1 half minus 1 end exponent minus 5 times 1 x to the power of 1 minus 1 end exponent end cell row blank equals cell x to the power of negative 1 half end exponent minus 5 x to the power of 0 end cell row blank equals cell 1 over x to the power of begin display style 1 half end style end exponent minus 5 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator square root of x end fraction minus 5 end cell end table  

Dengan demikian turunan pertama dari f open parentheses x close parentheses equals 11 plus 2 square root of x minus 5 x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator square root of x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table.

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