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Tentukan turunan pertama dari fungsi berikut. c.

Tentukan turunan pertama undefined dari fungsi berikut.

c. begin mathsize 14px style y equals x squared space ln open parentheses x squared minus 1 close parentheses end style 

Jawaban:

Gunakan konsep turunan perkalian dua fungsi dan turunan logaritma natural begin mathsize 14px style open parentheses ln close parentheses end style berikut:

begin mathsize 14px style y equals u times v rightwards double arrow y apostrophe equals u apostrophe v plus u v apostrophe y equals ln space g open parentheses x close parentheses rightwards double arrow y apostrophe equals fraction numerator g apostrophe open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction end style 

Akan ditentukan turunan pertama undefined dari fungsi begin mathsize 14px style y equals x squared space ln open parentheses x squared minus 1 close parentheses end style, perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row y equals cell x squared space ln open parentheses x squared minus 1 close parentheses end cell row cell fraction numerator straight d y over denominator straight d x end fraction end cell equals cell fraction numerator straight d over denominator straight d x end fraction open parentheses x squared close parentheses cross times ln open parentheses x squared minus 1 close parentheses plus x squared cross times fraction numerator straight d over denominator straight d x end fraction open parentheses ln open parentheses x squared minus 1 close parentheses close parentheses end cell row blank equals cell 2 x cross times ln open parentheses x squared minus 1 close parentheses plus x squared cross times fraction numerator 2 x over denominator x squared minus 1 end fraction end cell row cell fraction numerator straight d y over denominator straight d x end fraction end cell equals cell 2 x space ln open parentheses x squared minus 1 close parentheses plus fraction numerator 2 x cubed over denominator x squared minus 1 end fraction end cell end table end style 

Jadi, diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator straight d y over denominator straight d x end fraction end cell equals cell 2 x space ln open parentheses x squared minus 1 close parentheses plus fraction numerator 2 x cubed over denominator x squared minus 1 end fraction end cell end table end style.

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