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Misalkan , maka hasildari adalah ....

Misalkan begin mathsize 14px style straight f open parentheses straight x close parentheses equals 2 tan invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses end style, maka hasil dari begin mathsize 14px style straight f to the power of straight apostrophe left parenthesis straight x right parenthesis end style adalah ....

  1. begin mathsize 14px style sec squared invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses tan invisible function application straight x end style

  2. begin mathsize 14px style sec squared invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses square root of sec invisible function application straight x end root tan invisible function application straight x end style

  3. begin mathsize 14px style text 2sec end text squared invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses square root of sec invisible function application straight x end root tan invisible function application straight x end style

  4. begin mathsize 14px style sec squared invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses sec invisible function application straight x space tan invisible function application straight x end style

  5. begin mathsize 14px style 2 sec squared invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses sec invisible function application straight x space tan invisible function application straight x end style

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Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

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Jawaban

jawaban yang tepat adalah B.

jawaban yang tepat adalah B.

Pembahasan

Misal sehingga . Oleh karena itu, didapat perhitungan sebagai berikut. Perhatikan bahwa , maka didapat . Perhatikan perhitunganberikut! Dengan demikian, hasildari adalah . Jadi, jawaban yang tepat adalah B.

Misal begin mathsize 14px style straight g open parentheses straight x close parentheses equals square root of sec invisible function application straight x end root end style sehingga begin mathsize 14px style straight g open parentheses straight x close parentheses equals open parentheses sec invisible function application straight x close parentheses to the power of 1 half end exponent end style.

Oleh karena itu, didapat perhitungan sebagai berikut.

begin mathsize 14px style straight g to the power of straight apostrophe open parentheses straight x close parentheses equals 1 half open parentheses sec invisible function application straight x close parentheses to the power of 1 half minus 1 end exponent times sec invisible function application straight x space tan invisible function application straight x straight g to the power of straight apostrophe open parentheses straight x close parentheses equals 1 half open parentheses sec invisible function application straight x close parentheses to the power of open parentheses 1 half minus 1 close parentheses plus 1 end exponent tan invisible function application straight x straight g to the power of straight apostrophe open parentheses straight x close parentheses equals 1 half open parentheses sec invisible function application straight x close parentheses to the power of 1 half end exponent tan invisible function application straight x straight g to the power of straight apostrophe open parentheses straight x close parentheses equals 1 half square root of sec invisible function application straight x end root space tan invisible function application straight x end style

Perhatikan bahwa begin mathsize 14px style straight f open parentheses straight x close parentheses equals 2 tan invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses end style, maka didapat begin mathsize 14px style straight f open parentheses straight x close parentheses equals 2 tan space straight g open parentheses straight x close parentheses end style.

Perhatikan perhitungan berikut!

begin mathsize 14px style straight f to the power of straight apostrophe open parentheses straight x close parentheses equals 2 space sec squared invisible function application straight g open parentheses straight x close parentheses times straight g to the power of straight apostrophe open parentheses straight x close parentheses straight f to the power of straight apostrophe open parentheses straight x close parentheses equals 2 space sec squared invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses times 1 half square root of sec invisible function application straight x end root space tan invisible function application straight x straight f to the power of straight apostrophe open parentheses straight x close parentheses equals sec squared invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses square root of sec invisible function application straight x end root space tan invisible function application straight x end style

Dengan demikian, hasil dari begin mathsize 14px style straight f to the power of straight apostrophe left parenthesis straight x right parenthesis end style adalah begin mathsize 14px style sec squared invisible function application open parentheses square root of sec invisible function application straight x end root close parentheses square root of sec invisible function application straight x end root tan invisible function application straight x end style.

Jadi, jawaban yang tepat adalah B.

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