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Turunan pertama dari fungsi f(x)=tan(x2−2)​ adalah ....

Pertanyaan

Turunan pertama dari fungsi f left parenthesis x right parenthesis equals square root of tan open parentheses x squared minus 2 close parentheses end root adalah ....

  1. f apostrophe left parenthesis x right parenthesis equals x sec squared open parentheses x squared minus 2 close parentheses square root of tan open parentheses x squared minus 2 close parentheses end root

  2. f apostrophe left parenthesis x right parenthesis equals sec squared open parentheses x squared minus 2 close parentheses square root of tan open parentheses x squared minus 2 close parentheses end root

  3. f apostrophe left parenthesis x right parenthesis equals x square root of tan open parentheses x squared minus 2 close parentheses end root

  4. f apostrophe left parenthesis x right parenthesis equals fraction numerator x sec squared open parentheses x squared minus 2 close parentheses over denominator square root of tan open parentheses x squared minus 2 close parentheses end root end fraction

  5. f apostrophe left parenthesis x right parenthesis equals fraction numerator sec squared open parentheses x squared minus 2 close parentheses over denominator square root of tan open parentheses x squared minus 2 close parentheses end root end fraction

D. Natalia

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa bentuk f left parenthesis x right parenthesis equals square root of tan open parentheses x squared minus 2 close parentheses end root dapat diubah menjadi f open parentheses x close parentheses equals open parentheses tan open parentheses x squared minus 2 close parentheses close parentheses to the power of 1 half end exponent.

Dengan menggunakan aturan rantai, didapat perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell open parentheses tan open parentheses x squared minus 1 close parentheses close parentheses to the power of 1 half end exponent end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 1 half open parentheses tan left parenthesis x squared minus 2 right parenthesis close parentheses to the power of negative 1 half end exponent times sec squared open parentheses x squared minus 2 close parentheses times 2 x end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator x times sec squared open parentheses x squared minus 2 close parentheses over denominator open parentheses tan open parentheses x squared minus 2 close parentheses close parentheses to the power of 1 half end exponent end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator x sec squared open parentheses x squared minus 2 close parentheses over denominator square root of tan open parentheses x squared minus 2 close parentheses end root end fraction end cell end table

Dengan demikian, turunan pertama dari fungsi f left parenthesis x right parenthesis equals square root of tan open parentheses x squared minus 2 close parentheses end root adalah f apostrophe left parenthesis x right parenthesis equals fraction numerator x sec squared open parentheses x squared minus 2 close parentheses over denominator square root of tan open parentheses x squared minus 2 close parentheses end root end fraction.

Jadi, jawaban yang tepat adalah D.

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