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Tentukan turunan dari fungsi-fungsi berikut. D.

Tentukan turunan dari fungsi-fungsi berikut.

D. begin mathsize 14px style h open parentheses x close parentheses equals 6 x minus square root of x cubed end root plus 3 end style

  1. ...undefined 

  2. ...undefined 

Jawaban:

Ingat:

begin mathsize 14px style f open parentheses x close parentheses equals a x to the power of n end style, maka begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals fraction numerator d left parenthesis a x to the power of n right parenthesis over denominator d x end fraction equals a times n x to the power of n minus 1 end exponent end style.

Diketahui fungsi begin mathsize 14px style h open parentheses x close parentheses equals 6 x minus square root of x cubed end root plus 3 end style, maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell 6 x minus square root of x cubed end root plus 3 end cell row blank equals cell 6 x minus x to the power of 3 over 2 end exponent plus 3 end cell row cell h apostrophe left parenthesis x right parenthesis end cell equals cell 6 x to the power of 1 minus 1 end exponent minus open parentheses 3 over x x to the power of open parentheses 3 over 2 minus 1 close parentheses end exponent close parentheses plus 0 end cell row blank equals cell 6 x to the power of 0 minus 3 over 2 x to the power of 1 half end exponent end cell row blank equals cell 6 minus fraction numerator 3 square root of x over denominator 2 end fraction end cell end table end style 

Jadi, turunan begin mathsize 14px style h open parentheses x close parentheses equals 6 x minus square root of x cubed end root plus 3 end style adalah begin mathsize 14px style h apostrophe left parenthesis x right parenthesis equals 6 minus fraction numerator 3 square root of x over denominator 2 end fraction end style.

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