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Fungsi turunan dari .

Pertanyaan

Fungsi turunan dari f open parentheses x close parentheses equals fraction numerator 3 x minus 5 over denominator x minus 1 end fraction.

Pembahasan Soal:

Turunan dari f open parentheses x close parentheses equals fraction numerator u open parentheses x close parentheses over denominator v open parentheses x close parentheses end fraction adalah:

f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe open parentheses x close parentheses v open parentheses x close parentheses minus u open parentheses x close parentheses v apostrophe open parentheses x close parentheses over denominator open parentheses v open parentheses x close parentheses close parentheses squared end fraction

Akan dicari turunan dari f open parentheses x close parentheses equals fraction numerator 3 x minus 5 over denominator x minus 1 end fraction.

Misalkan :

table attributes columnalign right center left columnspacing 2px end attributes row cell u open parentheses x close parentheses end cell equals cell 3 x minus 5 end cell row cell v open parentheses x close parentheses end cell equals cell x minus 1 end cell end table

Sehingga diperoleh :

table attributes columnalign right center left columnspacing 2px end attributes row cell u apostrophe left parenthesis x right parenthesis end cell equals 3 row cell v apostrophe open parentheses x close parentheses end cell equals 1 end table

Turunan dari f open parentheses x close parentheses equals fraction numerator 3 x minus 5 over denominator x minus 1 end fraction adalah :

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

Jadi, fungsi turunan dari f open parentheses x close parentheses equals fraction numerator 3 x minus 5 over denominator x minus 1 end fraction adalah fraction numerator 2 over denominator x squared minus 2 x plus 1 end fraction.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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