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Pertanyaan

straight F left parenthesis x right parenthesis equals fraction numerator 2 x minus 3 over denominator x plus 5 end fraction comma space f apostrophe left parenthesis x right parenthesis equals ...

Pembahasan Soal:

Diketahui fungsi straight F left parenthesis x right parenthesis equals fraction numerator 2 x minus 3 over denominator x plus 5 end fraction.

Misalkan:

u equals 2 x minus 3 space rightwards arrow u apostrophe equals 2 v equals x plus 5 space rightwards arrow v apostrophe equals 1 

Turunan fungsi straight F left parenthesis x right parenthesis equals fraction numerator 2 x minus 3 over denominator x plus 5 end fraction:

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator 2 left parenthesis x plus 5 right parenthesis minus left parenthesis 2 x minus 3 right parenthesis 1 over denominator left parenthesis x plus 5 right parenthesis squared end fraction end cell row blank equals cell fraction numerator 2 x plus 10 minus 2 x plus 3 over denominator left parenthesis x plus 5 right parenthesis squared end fraction end cell row blank equals cell 13 over left parenthesis x plus 5 right parenthesis squared end cell end table

Jadi, turunan fungsi straight F left parenthesis x right parenthesis equals fraction numerator 2 x minus 3 over denominator x plus 5 end fraction adalah f apostrophe left parenthesis x right parenthesis equals 13 over open parentheses x plus 5 close parentheses squared.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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