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Tentukan turunan dari fungsi-fungsi berikut ini: f ( x ) = 3 x 2 + x 5 − x 2 ​

Tentukan turunan dari fungsi-fungsi berikut ini:

          

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Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Pembahasan

Gunakan konsep turunan pada pembagian dua fungsi: maka misalkan dan sehingga turunannya: kemudian substitusikan: Dengan demikian turunan dari fungsi adalah .

Gunakan konsep turunan pada pembagian dua fungsi:

table row cell f open parentheses x close parentheses equals a x to the power of n end cell rightwards arrow cell f apostrophe open parentheses x close parentheses equals a times n x to the power of n minus 1 end exponent end cell row cell f open parentheses x close parentheses equals a end cell rightwards arrow cell f apostrophe open parentheses x close parentheses equals 0 end cell row cell f open parentheses x close parentheses equals u over v end cell rightwards arrow cell f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end cell end table 

maka misalkan u equals 5 minus x squared dan v equals 3 x squared plus x sehingga turunannya:

table row cell u equals 5 minus x squared end cell rightwards arrow cell u apostrophe equals negative 2 x end cell row cell v equals 3 x squared plus x end cell rightwards arrow cell v apostrophe equals 6 x plus 1 end cell end table    

kemudian substitusikan:

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 x close parentheses open parentheses 3 x squared plus x close parentheses minus open parentheses 5 minus x squared close parentheses open parentheses 6 x plus 1 close parentheses over denominator open parentheses 3 x squared plus x close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 6 x cubed minus 2 x squared minus open parentheses 30 x plus 5 minus 6 x cubed minus x squared close parentheses over denominator open parentheses 3 x squared plus x close parentheses open parentheses 3 x squared plus x close parentheses end fraction end cell row blank equals cell fraction numerator negative 6 x cubed minus 2 x squared plus 6 x cubed plus x squared minus 30 x minus 5 over denominator 9 x to the power of 4 plus 3 x cubed plus 3 x cubed plus x squared end fraction end cell row blank equals cell fraction numerator negative x squared minus 30 x minus 5 over denominator 9 x to the power of 4 plus x squared plus 6 x cubed end fraction end cell end table       


Dengan demikian turunan dari fungsi f open parentheses x close parentheses equals fraction numerator 5 minus x squared over denominator 3 x squared plus x end fraction adalah 

f apostrophe open parentheses x close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative x squared minus 30 x minus 5 over denominator 9 x to the power of 4 plus x squared plus 6 x cubed end fraction end cell end table.

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