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Diketahui . Turunan pertama fungsi g adalah...

Pertanyaan

Diketahui begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator 5 x minus 1 over denominator 3 x plus 4 end fraction end style. Turunan pertama fungsi g adalah...

Pembahasan Soal:

Ingat rumus turunan aljabar begin mathsize 14px style y equals a x to the power of n rightwards arrow y apostrophe equals a n x to the power of n minus 1 end exponent end style  dan sifat turunan pada pembagian fungsi begin mathsize 14px style y equals u over v rightwards arrow y apostrophe equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight g left parenthesis straight x right parenthesis end cell equals cell fraction numerator 5 straight x minus 1 over denominator 3 straight x plus 4 end fraction end cell row cell straight g apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator 5 left parenthesis 3 straight x plus 4 right parenthesis minus left parenthesis 5 straight x minus 1 right parenthesis 3 over denominator left parenthesis 3 straight x plus 4 right parenthesis squared end fraction end cell row blank equals cell fraction numerator 15 straight x plus 20 minus 15 straight x plus 3 over denominator left parenthesis 3 straight x plus 4 right parenthesis squared end fraction end cell row blank equals cell 23 over left parenthesis 3 straight x plus 4 right parenthesis squared end cell end table end style

Jadi, diperoleh hasil turunannya adalah begin mathsize 14px style straight g apostrophe left parenthesis straight x right parenthesis equals 23 over left parenthesis 3 straight x plus 4 right parenthesis squared end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 April 2021

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