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Tentukan turunan pertama dari fungsi di bawah ini. 4. f ( x ) = 3 6 x 5 ​ + 5 5 x 7 ​ + 4 x ​

Tentukan turunan pertama dari fungsi di bawah ini.

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Untuk menentukan turunan dari fungsi tersebut, terlebih dahulu kita ubah ke dalam bentuk fungsi perpangkatan. Menentukan turunan pertamanya. Jadi,turunan pertama dari fungsi tersebut adalah .

Untuk menentukan turunan dari fungsi tersebut, terlebih dahulu kita ubah ke dalam bentuk fungsi perpangkatan.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell cube root of 6 x to the power of 5 end root plus fifth root of 5 x to the power of 7 end root plus square root of 4 x end root end cell row blank equals cell open parentheses 6 x to the power of 5 close parentheses to the power of 1 third end exponent plus open parentheses 5 x to the power of 7 close parentheses to the power of 1 fifth end exponent plus open parentheses 4 x close parentheses to the power of 1 half end exponent end cell row blank equals cell 6 to the power of 1 third end exponent x to the power of 5 over 3 end exponent plus 5 to the power of 1 fifth end exponent x to the power of 7 over 5 end exponent plus 2 x to the power of 1 half end exponent end cell end table end style 

Menentukan turunan pertamanya.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 5 over 3 times 6 to the power of 1 third end exponent x to the power of 5 over 3 minus 1 end exponent plus 7 over 5 times 5 to the power of 1 fifth end exponent x to the power of 7 over 5 minus 1 end exponent plus 1 half times 2 x to the power of 1 half minus 1 end exponent end cell row blank equals cell 5 over 3 times 6 to the power of 1 third end exponent x to the power of 2 over 3 end exponent plus 7 over 5 times 5 to the power of 1 fifth end exponent x to the power of 2 over 5 end exponent plus x to the power of negative 1 half end exponent end cell row blank equals cell 5 over 3 left parenthesis 6 x squared right parenthesis to the power of 1 third end exponent plus 7 over 5 left parenthesis 5 x squared right parenthesis to the power of 1 fifth end exponent plus fraction numerator 1 over denominator square root of x end fraction end cell row blank equals cell 5 over 3 cube root of 6 x squared end root plus 7 over 5 fifth root of 5 x squared end root plus fraction numerator 1 over denominator square root of x end fraction end cell end table end style    

Jadi, turunan pertama dari fungsi tersebut adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cube root of 6 x squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 7 over 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fifth root of 5 x squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus 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 end style.

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