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Diketahui fungsi  tentukan turunan pertama ...

Pertanyaan

Diketahui fungsi f open parentheses x close parentheses equals fraction numerator x squared plus 6 over denominator square root of x end fraction tentukan turunan pertama ...

Pembahasan Soal:

Ingat rumus turunan y equals u over v rightwards arrow y apostrophe equals fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction dan dimisalkan

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x squared plus 6 end cell row cell u apostrophe end cell equals cell 2 x end cell end table

dan

table attributes columnalign right center left columnspacing 0px end attributes row v equals cell square root of x end cell row v equals cell x to the power of 1 half end exponent end cell row cell v apostrophe end cell equals cell 1 half x to the power of 1 half minus 1 end exponent end cell row cell v apostrophe end cell equals cell 1 half x to the power of negative 1 half end exponent end cell end table

Sehingga diperoleh

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

Jadi, turunan pertama fungsi f open parentheses x close parentheses equals fraction numerator x squared plus 6 over denominator square root of x end fraction adalah f apostrophe open parentheses x close parentheses equals equals 3 over 2 square root of x minus fraction numerator 3 over denominator square root of x cubed end root end fraction.

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Mei 2021

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