Pertanyaan

Diketahui maka nilai y saat x = 2 1 adalah ….

Diketahui maka nilai $y$ saat $x = \frac{1}{2}$ adalah ….

S. Dwi

Master Teacher

Jawaban terverifikasi

Pembahasan

Turunan pertama: Turunan kedua: Misalkan: Maka, Sehingga nilai saat adalah : Maka, jawaban yang tepat adalah C.

Turunan pertama:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell tan invisible function application open parentheses 2 x minus 1 close parentheses end cell row cell y to the power of apostrophe end cell equals cell sec squared invisible function application open parentheses 2 x minus 1 close parentheses end cell row cell y to the power of apostrophe end cell equals cell fraction numerator 1 over denominator cos squared invisible function application open parentheses 2 x minus 1 close parentheses end fraction end cell end table end style$

Turunan kedua:

Misalkan:

Maka,

$begin mathsize 14px style y to the power of apostrophe apostrophe end exponent equals fraction numerator u to the power of apostrophe v minus u v to the power of apostrophe over denominator v squared end fraction y to the power of apostrophe apostrophe end exponent equals fraction numerator 0 times cos squared invisible function application open parentheses 2 x minus 1 close parentheses minus 1 times negative 4 cos invisible function application open parentheses 2 x minus 1 close parentheses sin invisible function application open parentheses 2 x minus 1 close parentheses over denominator cos to the power of 4 invisible function application open parentheses 2 x minus 1 close parentheses end fraction y to the power of apostrophe apostrophe end exponent equals fraction numerator 4 cos invisible function application open parentheses 2 x minus 1 close parentheses sin invisible function application open parentheses 2 x minus 1 close parentheses over denominator cos to the power of 4 invisible function application open parentheses 2 x minus 1 close parentheses end fraction y to the power of apostrophe apostrophe end exponent equals fraction numerator 4 sin invisible function application open parentheses 2 x minus 1 close parentheses over denominator cos cubed invisible function application open parentheses 2 x minus 1 close parentheses end fraction y to the power of apostrophe apostrophe end exponent equals fraction numerator 4 tan invisible function application open parentheses 2 x minus 1 close parentheses over denominator cos squared invisible function application open parentheses 2 x minus 1 close parentheses end fraction end style$

Sehingga nilai saat adalah :

$begin mathsize 14px style y to the power of apostrophe apostrophe end exponent equals fraction numerator 4 tan invisible function application open parentheses 2 open parentheses 1 half close parentheses minus 1 close parentheses over denominator cos squared invisible function application open parentheses 2 open parentheses 1 half close parentheses minus 1 close parentheses end fraction equals fraction numerator 4 tan invisible function application 0 over denominator cos invisible function application 0 end fraction equals fraction numerator 4 times 0 over denominator 1 end fraction equals 0 end style$

Maka, jawaban yang tepat adalah C.