Pertanyaan

Jika diberikan fungsi maka nilai dari ......

Jika diberikan fungsi $f open parentheses x close parentheses equals cos invisible function application open parentheses fraction numerator x squared minus 1 over denominator x plus 4 end fraction close parentheses space$ maka nilai dari ......

$fraction numerator x squared plus 8 x plus 1 over denominator open parentheses x plus 4 close parentheses squared end fraction space. sin invisible function application open parentheses fraction numerator x squared minus 1 over denominator x plus 4 end fraction close parentheses$
$sin invisible function application open parentheses fraction numerator x squared minus 1 over denominator x plus 4 end fraction close parentheses$
$fraction numerator 8 x plus 1 over denominator open parentheses x plus 4 close parentheses squared end fraction space. sin invisible function application open parentheses fraction numerator x squared minus 1 over denominator x plus 4 end fraction close parentheses$
$fraction numerator x squared plus 8 x plus 1 over denominator open parentheses x plus 4 close parentheses squared end fraction space. cos invisible function application open parentheses fraction numerator x squared minus 1 over denominator x plus 4 end fraction close parentheses$

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Pembahasan

Misalkan:

$y equals cos invisible function application open parentheses fraction numerator x squared minus 1 over denominator x plus 4 end fraction close parentheses$

Misalkan: $z equals fraction numerator x squared minus 1 over denominator x plus 4 end fraction rightwards arrow y equals cos invisible function application z$

$z equals fraction numerator x squared minus 1 over denominator x plus 4 end fraction table row cell right curly bracket u end cell row cell right curly bracket v end cell end table u equals x squared minus 1 space space semicolon space space u to the power of apostrophe equals 2 x v equals x plus 4 space space semicolon space v to the power of apostrophe equals 1 fraction numerator d z over denominator d x end fraction equals fraction numerator u to the power of apostrophe v minus u v to the power of apostrophe over denominator v squared end fraction fraction numerator d z over denominator d x end fraction equals fraction numerator 2 x open parentheses x plus 4 close parentheses minus open parentheses x squared minus 1 close parentheses 1 over denominator open parentheses x plus 4 close parentheses squared end fraction fraction numerator d z over denominator d x end fraction equals fraction numerator x squared plus 8 x plus 1 over denominator open parentheses x plus 4 close parentheses squared end fraction f to the power of apostrophe open parentheses x close parentheses equals fraction numerator d y over denominator d x end fraction equals fraction numerator d y over denominator d z end fraction fraction numerator d z over denominator d x end fraction f to the power of apostrophe open parentheses x close parentheses equals open parentheses negative sin invisible function application z close parentheses open parentheses fraction numerator x squared plus 8 x plus 1 over denominator open parentheses x plus 4 close parentheses squared end fraction close parentheses f to the power of apostrophe open parentheses x close parentheses equals negative fraction numerator x squared plus 8 x plus 1 over denominator open parentheses x plus 4 close parentheses squared end fraction sin invisible function application open parentheses fraction numerator x squared minus 1 over denominator x plus 4 end fraction close parentheses$