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Tentukan  dari fungsi-fungsi berikut. 1.

Pertanyaan

Tentukan f apostrophe left parenthesis x right parenthesis dari fungsi-fungsi berikut.

1. f left parenthesis x right parenthesis equals left parenthesis x squared plus 1 right parenthesis square root of left parenthesis x squared plus 1 right parenthesis end root 

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals left parenthesis x squared plus 1 right parenthesis square root of left parenthesis x squared plus 1 right parenthesis end root.

Misalkan u equals x squared plus 1 maka u apostrophe equals 2 x.

v equals square root of left parenthesis x squared plus 1 right parenthesis end root maka v apostrophe equals 1 half left parenthesis x squared plus 1 right parenthesis to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent times 2 x equals fraction numerator x over denominator square root of x squared plus 1 end root end fraction 

Turunan dari f left parenthesis x right parenthesis adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell u apostrophe v plus u v apostrophe end cell row blank equals cell 2 x square root of left parenthesis x squared plus 1 right parenthesis end root plus left parenthesis x squared plus 1 right parenthesis times fraction numerator x over denominator square root of left parenthesis x squared plus 1 right parenthesis end root end fraction end cell row blank equals cell 2 x square root of left parenthesis x squared plus 1 right parenthesis end root plus fraction numerator x left parenthesis x squared plus 1 right parenthesis over denominator square root of left parenthesis x squared plus 1 right parenthesis end root end fraction end cell row blank equals cell 2 x square root of left parenthesis x squared plus 1 right parenthesis end root plus x square root of left parenthesis x squared plus 1 right parenthesis end root end cell row blank equals cell 3 x square root of left parenthesis x squared plus 1 right parenthesis end root end cell end table 

Jadi, f apostrophe left parenthesis x right parenthesis equals 3 x square root of x squared plus 1 end root

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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