Pertanyaan

Tentukan turunan dari fungsi berikut. f ( x ) = ( x 2 + 5 ) ( 4 x − 1 )

Tentukan turunan dari fungsi berikut.

$f (x) = \frac{( 4 x - 1 )}{( x ^{2} + 5 )}$

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Diketahui ,misalkan , maka , sehingga Jadi, turunan dari adalah .

Diketahui $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator open parentheses 4 x minus 1 close parentheses over denominator open parentheses x squared plus 5 close parentheses end fraction end style$ , misalkan , maka , sehingga

$begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator open parentheses 4 x minus 1 close parentheses over denominator open parentheses x squared plus 5 close parentheses end fraction f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction space space space space space space space space equals fraction numerator 4 open parentheses x squared plus 5 close parentheses minus 2 x open parentheses 4 x minus 1 close parentheses over denominator open parentheses x squared plus 5 close parentheses squared end fraction space space space space space space space space equals fraction numerator 4 x squared plus 20 minus 8 x squared plus 2 x over denominator x to the power of 4 plus 10 x squared plus 25 end fraction space space space space space space space space equals fraction numerator negative 4 x squared plus 2 x plus 20 over denominator x to the power of 4 plus 10 x squared plus 25 end fraction end style$

Jadi, turunan dari $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator open parentheses 4 x minus 1 close parentheses over denominator open parentheses x squared plus 5 close parentheses end fraction end style$ adalah

$begin mathsize 14px style f apostrophe open parentheses x close parentheses space equals fraction numerator negative 4 x squared plus 2 x plus 20 over denominator x to the power of 4 plus 10 x squared plus 25 end fraction end style$ .