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Diketahui dan turunan pertama fungsi g ( x ) adalah g ( x ) . Rumus adalah ...

Diketahui g open parentheses x close parentheses equals left parenthesis 6 x cubed plus 2 x squared minus 5 x plus 3 right parenthesis to the power of 4 dan turunan pertama fungsi adalah . Rumus g apostrophe left parenthesis x right parenthesis adalah ...

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M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

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rumus adalah .

rumus g apostrophe left parenthesis x right parenthesis adalah g apostrophe left parenthesis x right parenthesis equals open parentheses 6 x cubed plus 2 x squared minus 5 x plus 3 close parentheses cubed times left parenthesis 72 x squared plus 16 x minus 20 right parenthesis.

Pembahasan

Ingat aturan rantai . Sehingga maka Jadi, rumus adalah .

Ingat aturan rantai g open parentheses x close parentheses equals open square brackets f open parentheses x close parentheses close square brackets to the power of n rightwards arrow g to the power of apostrophe left parenthesis x right parenthesis equals n times open square brackets f open parentheses x close parentheses close square brackets to the power of n minus 1 end exponent times f apostrophe left parenthesis x right parenthesis.

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 6 x cubed plus 2 x squared minus 5 x plus 3 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 18 x squared plus 4 x minus 5 end cell end table

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell g to the power of apostrophe left parenthesis x right parenthesis end cell equals cell n times open square brackets f open parentheses x close parentheses close square brackets to the power of n minus 1 end exponent times f apostrophe left parenthesis x right parenthesis end cell row blank equals cell 4 times open square brackets f open parentheses x close parentheses close square brackets to the power of 4 minus 1 end exponent times f apostrophe left parenthesis x right parenthesis end cell row blank equals cell 4 times open square brackets f open parentheses x close parentheses close square brackets cubed times f apostrophe left parenthesis x right parenthesis end cell row blank equals cell 4 times open parentheses 6 x cubed plus 2 x squared minus 5 x plus 3 close parentheses cubed times left parenthesis 18 x squared plus 4 x minus 5 right parenthesis end cell row blank equals cell open parentheses 6 x cubed plus 2 x squared minus 5 x plus 3 close parentheses cubed times left parenthesis 72 x squared plus 16 x minus 20 right parenthesis end cell end table

Jadi, rumus g apostrophe left parenthesis x right parenthesis adalah g apostrophe left parenthesis x right parenthesis equals open parentheses 6 x cubed plus 2 x squared minus 5 x plus 3 close parentheses cubed times left parenthesis 72 x squared plus 16 x minus 20 right parenthesis.

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