Carilah turunan pertama dari : f(x)=x+5x2−3x+1​

Pertanyaan

Carilah turunan pertama dari : f left parenthesis x right parenthesis equals fraction numerator x squared minus 3 x plus 1 over denominator x plus 5 end fraction

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Jawaban terverifikasi

Jawaban

turunan pertamanya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f apostrophe left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 10 x minus 16 over denominator x squared plus 10 x plus 25 end fraction end cell end table.

Pembahasan

Pembahasan

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x squared minus 3 x plus 1 end cell row cell u apostrophe end cell equals cell 2 x to the power of 2 minus 1 end exponent space minus space 3 x to the power of 1 minus 1 end exponent space end cell row cell u apostrophe end cell equals cell 2 x to the power of 1 minus 3 x to the power of 0 end cell row cell u apostrophe end cell equals cell 2 x minus 3 end cell row blank blank blank row v equals cell x plus 5 end cell row cell v apostrophe end cell equals cell x to the power of 1 minus 1 end exponent space end cell row cell v apostrophe end cell equals cell x to the power of 0 end cell row cell v apostrophe end cell equals 1 row blank blank blank row cell f left parenthesis x right parenthesis end cell equals cell u over v end cell 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 cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator open parentheses 2 x minus 3 close parentheses open parentheses x plus 5 close parentheses minus open parentheses x squared minus 3 x plus 1 close parentheses open parentheses 1 close parentheses over denominator open parentheses x plus 5 close parentheses squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator open parentheses 2 x squared plus 10 x minus 3 x minus 15 close parentheses minus open parentheses x squared minus 3 x plus 1 close parentheses over denominator open parentheses x plus 5 close parentheses squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x squared plus 7 x minus 15 minus x squared plus 3 x minus 1 over denominator open parentheses x plus 5 close parentheses squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x squared minus x squared plus 7 x plus 3 x minus 15 minus 1 over denominator open parentheses x plus 5 close parentheses squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator x squared plus 10 x minus 16 over denominator x squared plus 10 x plus 25 end fraction end cell end table
 

Jadi, turunan pertamanya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f apostrophe left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 10 x minus 16 over denominator x squared plus 10 x plus 25 end fraction end cell end table.

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