Pertanyaan

Jika dan ,maka nilai dari adalah ....

Jika $f open parentheses x close parentheses equals fraction numerator cos x over denominator sin x plus cos x end fraction$ dan $f apostrophe apostrophe open parentheses x close parentheses equals fraction numerator a cos 2 x over denominator open parentheses sin 2 x plus b close parentheses squared end fraction$ , maka nilai dari open parentheses a over b close parentheses squared adalah ....

D. Natalia

Master Teacher

Jawaban terverifikasi

Pembahasan

Misalkan u = cos x dan v = sin x + cos x , maka u ' = - sin x dan v = cos x - sin x . sehingga Jika nilai a = 2 dan b = 1 sehingga

Misalkan u = cos x dan v = sin x + cos x, maka u' = -sin x dan v = cos x - sin x. sehingga

$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 fraction numerator cos invisible function application x over denominator sin invisible function application x plus cos invisible function application x end fraction equals u over v end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator u to the power of apostrophe v minus u v to the power of apostrophe over denominator v squared end fraction end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator negative sin invisible function application x open parentheses sin invisible function application x plus cos invisible function application x close parentheses minus cos invisible function application x open parentheses cos invisible function application x minus sin invisible function application x close parentheses over denominator open parentheses sin invisible function application x plus cos invisible function application x close parentheses squared end fraction end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator negative sin squared invisible function application x minus sin invisible function application x cos invisible function application x minus cos squared invisible function application x plus sin invisible function application x cos invisible function application x over denominator sin squared invisible function application x plus 2 sin invisible function application x cos invisible function application x plus cos squared invisible function application x end fraction end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator negative sin squared invisible function application x minus sin invisible function application x cos invisible function application x minus cos squared invisible function application x plus sin invisible function application x cos invisible function application x over denominator sin squared invisible function application x plus 2 sin invisible function application x cos invisible function application x plus cos squared invisible function application x end fraction end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator negative open parentheses sin squared invisible function application x plus cos squared invisible function application x close parentheses over denominator 1 plus sin invisible function application 2 x end fraction end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell negative fraction numerator 1 over denominator 1 plus sin invisible function application 2 x end fraction end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell negative open parentheses 1 plus sin invisible function application 2 x close parentheses to the power of negative 1 end exponent end cell row cell f to the power of apostrophe apostrophe end exponent open parentheses x close parentheses end cell equals cell negative open parentheses negative 1 close parentheses open parentheses 1 plus sin invisible function application 2 x close parentheses to the power of negative 2 end exponent open parentheses cos invisible function application 2 x close parentheses open parentheses 2 close parentheses end cell row cell f to the power of apostrophe apostrophe end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2 cos invisible function application 2 x over denominator open parentheses 1 plus sin invisible function application 2 x close parentheses squared end fraction end cell end table end style$

Jika nilai a = 2 dan b = 1 sehingga