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Diketahui fungsi f dinyatakan oleh f ( x ) = sin ( 2 x + π ) cos ( 2 x − π ) Turunan pertama dari yaitu f . Tentukan: b. nilai f ( 2 π ​ )

Diketahui fungsi  dinyatakan oleh

 

Turunan pertama dari f yaitu . Tentukan:

b. nilai 

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P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

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diperoleh nilai .

diperoleh nilai 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 straight pi over 2 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 2 end table.

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Pembahasan

Ingat kembali aturan turunan fungsi trigonometri berikut. Misalkan: Sehingga dapat ditentukan nilai dari sebagai berikut. Dengan demikian, diperoleh nilai .

Ingat kembali aturan turunan fungsi trigonometri berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell h open parentheses x close parentheses times g open parentheses x close parentheses rightwards double arrow f apostrophe open parentheses x close parentheses equals h apostrophe open parentheses x close parentheses times g open parentheses x close parentheses plus h open parentheses x close parentheses times g apostrophe open parentheses x close parentheses end cell row cell f open parentheses x close parentheses end cell equals cell sin space open parentheses a x plus c close parentheses rightwards double arrow f apostrophe open parentheses x close parentheses equals a space cos space open parentheses a x plus c close parentheses end cell row cell f open parentheses x close parentheses end cell equals cell cos space open parentheses b x plus c close parentheses rightwards double arrow f apostrophe open parentheses x close parentheses equals negative b space sin space open parentheses b x plus c close parentheses end cell end table 

Misalkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell h open parentheses x close parentheses end cell equals cell sin space open parentheses 2 x plus straight pi close parentheses rightwards double arrow h apostrophe open parentheses x close parentheses equals 2 space cos space open parentheses 2 x plus straight pi close parentheses end cell row cell g open parentheses x close parentheses end cell equals cell cos space open parentheses 2 x minus straight pi close parentheses rightwards double arrow g apostrophe open parentheses x close parentheses equals negative 2 space sin space open parentheses 2 x minus straight pi close parentheses end cell end table

Sehingga dapat ditentukan nilai dari f apostrophe open parentheses straight pi over 2 close parentheses sebagai berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell sin space left parenthesis 2 straight x plus straight pi right parenthesis times cos space left parenthesis 2 straight x minus straight pi right parenthesis end cell row blank equals cell h left parenthesis x right parenthesis times g left parenthesis x right parenthesis end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell h apostrophe left parenthesis x right parenthesis times g left parenthesis x right parenthesis plus h left parenthesis x right parenthesis times g apostrophe left parenthesis x right parenthesis end cell row blank equals cell 2 cos space open parentheses 2 straight x plus straight pi close parentheses times cos space open parentheses 2 straight x minus straight pi close parentheses plus sin space open parentheses 2 straight x plus straight pi close parentheses times open parentheses negative 2 times sin space open parentheses 2 straight x minus straight pi close parentheses close parentheses end cell row blank equals cell 2 cos space left parenthesis 2 straight x plus straight pi right parenthesis times cos space left parenthesis 2 straight x minus straight pi right parenthesis minus 2 times sin space left parenthesis 2 straight x plus straight pi right parenthesis times sin space left parenthesis 2 straight x minus straight pi right parenthesis end cell row blank equals cell 2 left parenthesis cos space open parentheses 2 straight x plus straight pi close parentheses times cos space open parentheses 2 straight x minus straight pi close parentheses minus sin space open parentheses 2 straight x plus straight pi close parentheses times sin space open parentheses 2 straight x minus straight pi close parentheses right parenthesis end cell row blank equals cell 2 times cos space left parenthesis open parentheses 2 straight x plus up diagonal strike straight pi close parentheses plus open parentheses 2 straight x minus up diagonal strike straight pi close parentheses right parenthesis end cell row blank equals cell 2 space cos space 4 straight x end cell row cell f apostrophe open parentheses straight pi over 2 close parentheses end cell equals cell 2 space cos space 4 open parentheses straight pi over 2 close parentheses end cell row blank equals cell 2 space cos space 2 straight pi end cell row blank equals cell 2 times 1 end cell row blank equals 2 end table end style

Dengan demikian, diperoleh nilai 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 straight pi over 2 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 2 end table.

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