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Pertanyaan

Selesaikan turunan deferensial dari y = x 2 1 ​ 2 ​ + x 2 1 ​ 6 ​ − x 2 3 ​ 2 ​ − x 2 3 ​ 4 ​ !

Selesaikan turunan deferensial dari !

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H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

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Jawaban

turunannya adalah .

turunannya adalah begin mathsize 14px style y apostrophe equals negative 1 over x to the power of begin display style 3 over 2 end style end exponent minus 3 over x to the power of begin display style 3 over 2 end style end exponent plus 3 over x to the power of begin display style 5 over 2 end style end exponent plus 6 over x to the power of begin display style 5 over 2 end style end exponent end style.

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Pembahasan

Jika dengan adalah konstanta real, maka . Sehingga kita ubah dahulu persamaan diatas menjadi . Kemudian kita cari turunannya. Jadi, turunannya adalah .

Jika begin mathsize 14px style y equals straight c x to the power of straight n end style dengan begin mathsize 14px style straight c comma space straight n end style adalah konstanta real, maka begin mathsize 14px style y apostrophe equals cn x to the power of straight n minus 1 end exponent end style. Sehingga kita ubah dahulu persamaan diatas menjadi begin mathsize 14px style y equals 2 x to the power of negative 1 half end exponent plus 6 x to the power of negative 1 half end exponent minus 2 x to the power of negative 3 over 2 end exponent minus 4 x to the power of negative 3 over 2 end exponent end style. Kemudian kita cari turunannya.

begin mathsize 9px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 x to the power of negative 1 half end exponent plus 6 x to the power of negative 1 half end exponent minus 2 x to the power of negative 3 over 2 end exponent minus 4 x to the power of negative 3 over 2 end exponent end cell row cell y apostrophe end cell equals cell 2 open parentheses negative 1 half close parentheses x to the power of negative 1 half minus 1 end exponent plus 6 open parentheses negative 1 half close parentheses x to the power of negative 1 half minus 1 end exponent minus 2 open parentheses negative 3 over 2 close parentheses x to the power of negative 3 over 2 minus 1 end exponent minus 4 open parentheses negative 3 over 2 close parentheses x to the power of negative 3 over 2 minus 1 end exponent end cell row blank equals cell negative x to the power of negative 3 over 2 end exponent minus 3 x to the power of negative 3 over 2 end exponent plus 3 x to the power of negative 5 over 2 end exponent plus 6 x to the power of negative 5 over 2 end exponent end cell row blank equals cell negative 1 over x to the power of begin display style 3 over 2 end style end exponent minus 3 over x to the power of begin display style 3 over 2 end style end exponent plus 3 over x to the power of begin display style 5 over 2 end style end exponent plus 6 over x to the power of begin display style 5 over 2 end style end exponent end cell end table end style

Jadi, turunannya adalah begin mathsize 14px style y apostrophe equals negative 1 over x to the power of begin display style 3 over 2 end style end exponent minus 3 over x to the power of begin display style 3 over 2 end style end exponent plus 3 over x to the power of begin display style 5 over 2 end style end exponent plus 6 over x to the power of begin display style 5 over 2 end style end exponent end style.

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