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Carilah turunan fungsi aljabar berikut ini:

Carilah turunan fungsi aljabar berikut ini:

begin mathsize 14px style y equals f left parenthesis x right parenthesis equals open parentheses x squared minus 2 x plus 1 close parentheses squared end style 

Jawaban:

Ingat!

Aturan Rantai:

begin mathsize 14px style y equals open parentheses g open parentheses x close parentheses close parentheses to the power of n comma space maka space y apostrophe equals n times open parentheses g open parentheses x close parentheses close parentheses to the power of n minus 1 end exponent times g apostrophe left parenthesis x right parenthesis end style 

Dengan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fungsi space awal end cell row cell y apostrophe end cell equals cell turunan space pertama space fungsi space y end cell row cell g open parentheses x close parentheses end cell equals cell fungsi space yang space dipangkatkan end cell row cell g apostrophe open parentheses x close parentheses end cell equals cell turunan space pertama space fungsi space g left parenthesis x right parenthesis end cell end table end style 

Diketahui begin mathsize 14px style y equals f left parenthesis x right parenthesis equals open parentheses x squared minus 2 x plus 1 close parentheses squared end style, maka:

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 x squared minus 2 x plus 1 end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 2 times x to the power of 2 minus 1 end exponent minus 2 x to the power of 1 minus 1 end exponent plus 0 end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 2 x minus 2 end cell end table end style 

Sehingga turunan pertama fungsi begin mathsize 14px style y end style adalah:

begin mathsize 14px style y apostrophe equals n times open parentheses g open parentheses x close parentheses close parentheses to the power of n minus 1 end exponent times g apostrophe open parentheses x close parentheses y apostrophe equals 2 times open parentheses x squared minus 2 x plus 1 close parentheses to the power of 2 minus 1 end exponent times open parentheses 2 x minus 2 close parentheses y apostrophe equals 2 open parentheses 2 x minus 2 close parentheses open parentheses x squared minus 2 x plus 1 close parentheses y apostrophe equals open parentheses 4 x minus 4 close parentheses open parentheses x squared minus 2 x plus 1 close parentheses end style  

Jadi, turunan pertama fungsi begin mathsize 14px style y end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 4 x minus 4 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x squared minus 2 x plus 1 right parenthesis end cell end table end style.

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