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Tentukan turunan pertama dari fungsi .

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Tentukan turunan pertama dari fungsi begin mathsize 14px style y equals fraction numerator x squared plus 2 x over denominator x minus 1 end fraction end style.

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Pembahasan Video:

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style y equals fraction numerator x squared plus 2 x over denominator x minus 1 end fraction end style. Dimisalkan:

begin mathsize 14px style g left parenthesis x right parenthesis equals x squared plus 2 x rightwards arrow g apostrophe left parenthesis x right parenthesis equals 2 x plus 2 h left parenthesis x right parenthesis equals x minus 1 space space space space rightwards arrow h apostrophe left parenthesis x right parenthesis equals 1 end style

Turunan pertama dari fungsi begin mathsize 14px style y end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator g left parenthesis x right parenthesis over denominator h left parenthesis x right parenthesis end fraction end cell row cell y apostrophe end cell equals cell fraction numerator g apostrophe left parenthesis x right parenthesis times h left parenthesis x right parenthesis minus g left parenthesis x right parenthesis times h apostrophe left parenthesis x right parenthesis over denominator h squared left parenthesis x right parenthesis end fraction end cell row cell y apostrophe end cell equals cell fraction numerator left parenthesis 2 x plus 2 right parenthesis left parenthesis x minus 1 right parenthesis minus open parentheses x squared plus 2 x close parentheses over denominator left parenthesis x minus 1 right parenthesis squared end fraction end cell row cell y apostrophe end cell equals cell fraction numerator 2 x squared minus 2 x plus 2 x minus 2 minus x squared minus 2 x over denominator left parenthesis x minus 1 right parenthesis squared end fraction end cell row cell y apostrophe end cell equals cell fraction numerator x squared minus 2 x minus 2 over denominator left parenthesis x minus 1 right parenthesis squared end fraction end cell end table end style

Jadi diperoleh turunan pertama dari fungsi begin mathsize 14px style y end style adalah begin mathsize 14px style y apostrophe equals fraction numerator x squared minus 2 x minus 2 over denominator open parentheses x minus 1 close parentheses squared end fraction end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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