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Pertanyaan

Tentukan turunan dari fungsi-fungsi berikut ini:

f open parentheses x close parentheses equals 11 plus 2 square root of x minus 5 x 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

turunan pertama dari f open parentheses x close parentheses equals 11 plus 2 square root of x minus 5 x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses 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 1 over denominator square root of x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table.

Pembahasan

Gunakan konsep turunan fungsi aljabar:

table row cell f open parentheses x close parentheses equals a x to the power of n end cell rightwards arrow cell f apostrophe open parentheses x close parentheses equals a times n x to the power of n minus 1 end exponent end cell row cell f open parentheses x close parentheses equals a end cell rightwards arrow cell f apostrophe open parentheses x close parentheses equals 0 end cell end table

sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 11 plus 2 square root of x minus 5 x end cell row cell f open parentheses x close parentheses end cell equals cell 11 plus 2 x to the power of 1 half end exponent minus 5 x end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 0 plus 2 times 1 half x to the power of 1 half minus 1 end exponent minus 5 times 1 x to the power of 1 minus 1 end exponent end cell row blank equals cell x to the power of negative 1 half end exponent minus 5 x to the power of 0 end cell row blank equals cell 1 over x to the power of begin display style 1 half end style end exponent minus 5 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator square root of x end fraction minus 5 end cell end table  

Dengan demikian turunan pertama dari f open parentheses x close parentheses equals 11 plus 2 square root of x minus 5 x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses 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 1 over denominator square root of x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table.

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