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Carilah turunan pertama, kedua dan ketiga dari: a. y = e − 4 x cos ( 2 x )

Carilah turunan pertama, kedua dan ketiga dari:

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begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell e to the power of negative 4 x end exponent cos left parenthesis 2 x right parenthesis end cell row cell y apostrophe end cell equals cell e to the power of negative 4 x end exponent left parenthesis negative 4 right parenthesis times cos space left parenthesis 2 x right parenthesis plus e to the power of negative 4 x end exponent times left parenthesis negative sin open parentheses 2 x close parentheses right parenthesis times 2 end cell row blank equals cell negative 4 e to the power of negative 4 x end exponent cos left parenthesis 2 x right parenthesis space minus 2 e to the power of negative 4 x end exponent sin left parenthesis 2 x right parenthesis end cell row blank blank blank row cell y " end cell equals cell left square bracket negative 4 times e to the power of negative 4 x end exponent times open parentheses negative 4 close parentheses times cos open parentheses 2 x close parentheses plus open parentheses negative 4 e to the power of negative 4 x end exponent close parentheses times open parentheses negative sin open parentheses 2 x close parentheses times 2 close parentheses right square bracket minus end cell row blank blank cell left square bracket 2 e to the power of negative 4 x end exponent times open parentheses negative 4 close parentheses times sin open parentheses 2 x close parentheses plus 2 e to the power of negative 4 x end exponent times left parenthesis cos space open parentheses 2 x close parentheses times 2 right parenthesis right square bracket end cell row blank equals cell 16 e to the power of negative 4 x end exponent cos left parenthesis 2 x right parenthesis plus 8 e to the power of negative 4 x end exponent sin left parenthesis 2 x right parenthesis plus 8 e to the power of negative 4 x end exponent sin left parenthesis 2 x right parenthesis minus 4 e to the power of negative 4 x end exponent cos left parenthesis 2 x right parenthesis end cell row blank equals cell 12 e to the power of negative 4 x end exponent cos left parenthesis 2 x right parenthesis plus 16 e to the power of negative 4 x end exponent sin left parenthesis 2 x right parenthesis end cell row blank blank blank row cell y apostrophe apostrophe apostrophe end cell equals cell left square bracket negative 48 e to the power of negative 4 x end exponent cos open parentheses 2 x close parentheses plus 12 e to the power of negative 4 x end exponent open parentheses negative 2 sin open parentheses 2 x close parentheses close parentheses right square bracket plus left square bracket negative 64 e to the power of negative 4 x end exponent sin open parentheses 2 x close parentheses plus right square bracket end cell row blank blank cell 16 e to the power of negative 4 x end exponent left parenthesis 2 cos open parentheses 2 x close parentheses right parenthesis end cell row blank equals cell negative 48 e to the power of negative 4 x end exponent cos left parenthesis 2 x right parenthesis minus 24 e to the power of negative 4 x end exponent sin left parenthesis 2 x right parenthesis minus 64 e to the power of negative 4 x end exponent sin left parenthesis 2 x right parenthesis plus 32 e to the power of negative 4 x end exponent cos left parenthesis 2 x right parenthesis end cell row blank equals cell negative 16 e to the power of negative 4 x end exponent cos left parenthesis 2 x right parenthesis minus 88 e to the power of negative 4 x end exponent sin left parenthesis 2 x right parenthesis end cell end table end style

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