Roboguru

Tentukan turunan   fungsi berikut

Pertanyaan

Tentukan turunan f apostrophe open parentheses x close parentheses  fungsi berikut

f open parentheses x close parentheses equals fraction numerator 2 x over denominator square root of 3 minus 2 x end root end fraction  

Pembahasan Soal:

Soal berikut dapat dikerjakan dengan turunan pembagian dua fungsi, seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 2 x over denominator square root of 3 minus 2 x end root end fraction end cell row y equals cell u over v end cell row cell y apostrophe end cell equals cell fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell row u equals cell 2 x end cell row cell u apostrophe end cell equals 2 row v equals cell square root of 3 minus 2 x end root end cell row blank equals cell open parentheses 3 minus 2 x close parentheses to the power of 1 divided by 2 end exponent end cell row cell v apostrophe end cell equals cell 1 half open parentheses 3 minus 2 x close parentheses to the power of negative 1 divided by 2 end exponent end cell row cell y apostrophe end cell equals cell fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell row blank equals cell fraction numerator 2 open parentheses 3 minus 2 x close parentheses to the power of begin display style 1 half end style end exponent minus begin display style 1 half end style open parentheses 3 minus 2 x close parentheses to the power of negative begin display style 1 half end style end exponent times 2 x over denominator open parentheses open parentheses 3 minus 2 x close parentheses to the power of begin display style 1 half end style end exponent close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 times open parentheses 3 minus 2 x close parentheses to the power of begin display style 1 half end style end exponent minus open parentheses 3 minus 2 x close parentheses to the power of negative begin display style 1 half end style end exponent times x over denominator 3 minus 2 x end fraction end cell row blank equals cell fraction numerator 2 square root of 3 minus 2 x end root minus x over denominator 3 minus 2 x open parentheses square root of 3 minus 2 x end root close parentheses end fraction end cell row blank equals cell fraction numerator 2 square root of 3 minus 2 x end root minus x over denominator square root of open parentheses 3 minus 2 x close parentheses cubed end root end fraction end cell end table

Jadi, nilai turunan dari persamaan tersebut adalah fraction numerator 2 square root of 3 minus 2 x end root minus x over denominator square root of open parentheses 3 minus 2 x close parentheses cubed end root end fraction

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 09 Juni 2021

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