Tentukan turunan pertama dari masing-masing fungsi berikut. b. y=x(x−3)(x+5)6

Pertanyaan

Tentukan turunan pertama dari masing-masing fungsi berikut.

b. y equals x open parentheses x minus 3 close parentheses open parentheses x plus 5 close parentheses to the power of 6  

N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

Jawaban terverifikasi

Jawaban

turunan pertama dari y equals x open parentheses x minus 3 close parentheses open parentheses x plus 5 close parentheses to the power of 6  adalah y apostrophe equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x plus 5 right parenthesis to the power of 5 space left parenthesis 8 x squared minus 11 x minus 15 right parenthesis end cell end table.

Pembahasan

y equals x open parentheses x minus 3 close parentheses open parentheses x plus 5 close parentheses to the power of 6 equals open parentheses x squared minus 3 x close parentheses open parentheses x plus 5 close parentheses to the power of 6 

Dimisalkan 

u equals x squared minus 3 x space rightwards arrow u apostrophe equals 2 x minus 3 v equals left parenthesis x plus 5 right parenthesis to the power of 6 space rightwards arrow space v apostrophe equals 6 left parenthesis x plus 5 right parenthesis to the power of 5 left parenthesis 1 right parenthesis equals 6 left parenthesis x plus 5 right parenthesis to the power of 5 

Dengan aturan hasil kali dalam turunan, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe end cell equals cell u apostrophe v plus u v apostrophe end cell row blank equals cell left parenthesis 2 x minus 3 right parenthesis left parenthesis x plus 5 right parenthesis to the power of 6 plus left parenthesis x squared minus 3 x right parenthesis left parenthesis 6 left parenthesis x plus 5 right parenthesis to the power of 5 right parenthesis end cell row blank equals cell left parenthesis 2 x minus 3 right parenthesis left parenthesis x plus 5 right parenthesis to the power of 6 plus left parenthesis 6 x squared minus 18 x right parenthesis left parenthesis x plus 5 right parenthesis to the power of 5 space end cell row blank equals cell left parenthesis x plus 5 right parenthesis to the power of 5 space left parenthesis left parenthesis x plus 5 right parenthesis left parenthesis 2 x minus 3 right parenthesis plus left parenthesis 6 x squared minus 18 x right parenthesis right parenthesis end cell row blank equals cell left parenthesis x plus 5 right parenthesis to the power of 5 space left parenthesis 2 x squared minus 3 x plus 10 x minus 15 plus 6 x squared minus 18 x right parenthesis end cell row blank equals cell left parenthesis x plus 5 right parenthesis to the power of 5 space left parenthesis 8 x squared minus 11 x minus 15 right parenthesis end cell row blank blank blank end table 

Dengan demikian, turunan pertama dari y equals x open parentheses x minus 3 close parentheses open parentheses x plus 5 close parentheses to the power of 6  adalah y apostrophe equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x plus 5 right parenthesis to the power of 5 space left parenthesis 8 x squared minus 11 x minus 15 right parenthesis end cell end table.

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