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Tentukan turunan dari fungsi-fungsi berikut. C.

Tentukan turunan dari fungsi-fungsi berikut.

C. begin mathsize 14px style g open parentheses x close parentheses equals cube root of 3 x squared end root end style

  1. ...undefined 

  2. ...undefined 

Jawaban:

Ingat:

begin mathsize 14px style f left parenthesis x right parenthesis equals a x to the power of n comma space maka space f apostrophe left parenthesis x right parenthesis equals a times n x to the power of n minus 1 end exponent end style.

Sehingga diperoleh,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell cube root of 3 x squared end root end cell row cell g left parenthesis x right parenthesis end cell equals cell 3 to the power of 1 third end exponent times x to the power of 2 over 3 end exponent end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 3 to the power of 1 third end exponent times 2 over 3 times x to the power of 2 over 3 minus 1 end exponent end cell row blank equals cell 3 to the power of 1 third minus 1 end exponent times 2 times x to the power of negative 1 third end exponent end cell row blank equals cell 3 to the power of negative 2 over 3 end exponent times 2 times fraction numerator 1 over denominator cube root of x end fraction end cell row blank equals cell fraction numerator 1 over denominator cube root of 3 squared end root end fraction times 2 times fraction numerator 1 over denominator cube root of x end fraction end cell row blank equals cell fraction numerator 2 over denominator cube root of 9 x end root end fraction end cell end table end style 

 

Jadi, turunan begin mathsize 14px style g open parentheses x close parentheses equals cube root of 3 x squared end root end style adalah begin mathsize 14px style g apostrophe left parenthesis x right parenthesis equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 over denominator cube root of 9 x end root end fraction end cell end table end style.

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