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Pertanyaan

Jika , maka ....

Jika begin mathsize 14px style f open parentheses x close parentheses equals cos invisible function application open parentheses sin squared invisible function application x close parentheses end style, maka begin mathsize 14px style f to the power of apostrophe apostrophe end exponent open parentheses 0 close parentheses equals end style....

  1. -π

  2. -1

  3. 0

  4. 1

  5. π

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R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa Misalkan dan maka Perhatikan bahwa Perhatikan pula bahwa dan Sehingga Jadi, jawaban yang tepat adalah C.

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell cos invisible function application left parenthesis sin squared invisible function application x right parenthesis end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell negative sin invisible function application left parenthesis sin squared invisible function application x right parenthesis bullet 2 sin invisible function application x bullet cos invisible function application x end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell negative sin invisible function application left parenthesis sin squared invisible function application x right parenthesis bullet sin invisible function application 2 x end cell end table end style

Misalkan begin mathsize 14px style u left parenthesis x right parenthesis equals negative sin invisible function application left parenthesis sin squared invisible function application x right parenthesis end style dan begin mathsize 14px style v left parenthesis x right parenthesis equals sin invisible function application 2 x comma end style maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell u left parenthesis x right parenthesis v left parenthesis x right parenthesis end cell row cell f apostrophe apostrophe left parenthesis x right parenthesis end cell equals cell u apostrophe left parenthesis x right parenthesis v left parenthesis x right parenthesis plus u left parenthesis x right parenthesis v apostrophe left parenthesis x right parenthesis end cell end table end style

Perhatikan bahwa

begin mathsize 14px style f apostrophe apostrophe left parenthesis 0 right parenthesis equals u apostrophe left parenthesis 0 right parenthesis v left parenthesis 0 right parenthesis plus u left parenthesis 0 right parenthesis v apostrophe left parenthesis 0 right parenthesis end style

Perhatikan pula bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell u left parenthesis x right parenthesis end cell equals cell negative sin invisible function application left parenthesis sin squared invisible function application x right parenthesis end cell row cell u left parenthesis 0 right parenthesis end cell equals cell negative sin invisible function application left parenthesis sin squared invisible function application 0 right parenthesis end cell row blank equals cell negative sin invisible function application left parenthesis 0 right parenthesis end cell row blank equals 0 end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell v left parenthesis x right parenthesis end cell equals cell sin invisible function application 2 x end cell row cell v left parenthesis 0 right parenthesis end cell equals cell sin invisible function application 2 left parenthesis 0 right parenthesis end cell row blank equals 0 end table end style

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe apostrophe left parenthesis 0 right parenthesis end cell equals cell u apostrophe left parenthesis 0 right parenthesis v left parenthesis 0 right parenthesis plus u left parenthesis 0 right parenthesis v apostrophe left parenthesis 0 right parenthesis end cell row blank equals cell u apostrophe left parenthesis 0 right parenthesis bullet 0 plus 0 bullet v apostrophe left parenthesis 0 right parenthesis end cell row blank equals cell 0 plus 0 end cell row blank equals 0 end table end style

Jadi, jawaban yang tepat adalah C.

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