Pertanyaan

Jika f ( x ) = sin x 1 + cos x maka f ( 2 π ) = ...

Jika $f (x) = \frac{1 + cos x}{sin x}$ maka $f (\frac{π}{2}) = ...$

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Jawaban terverifikasi

Jawaban

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f apostrophe open parentheses straight pi over 2 close parentheses equals negative 1

Pembahasan

Mencari turunan dari : Mencari : Jadi, .

Mencari turunan dari $f left parenthesis x right parenthesis equals fraction numerator 1 plus cos space x over denominator sin space x end fraction$ :

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator straight d over denominator straight d x end fraction left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell fraction numerator straight d over denominator straight d x end fraction open parentheses fraction numerator 1 plus cos open parentheses x close parentheses over denominator sin open parentheses x close parentheses end fraction close parentheses end cell row blank equals cell fraction numerator straight d over denominator straight d x end fraction open parentheses cot open parentheses x close parentheses plus csc open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator straight d over denominator straight d x end fraction open parentheses cot open parentheses x close parentheses close parentheses plus fraction numerator straight d over denominator straight d x end fraction open parentheses csc open parentheses x close parentheses close parentheses end cell row blank equals cell negative csc squared open parentheses x close parentheses minus cot open parentheses x close parentheses csc open parentheses x close parentheses end cell end table$

Mencari f apostrophe open parentheses straight pi over 2 close parentheses :

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses straight pi over 2 close parentheses end cell equals cell negative csc squared open parentheses x close parentheses minus cot open parentheses x close parentheses csc open parentheses x close parentheses end cell row blank equals cell negative csc squared open parentheses 90 degree close parentheses minus cot open parentheses 90 degree close parentheses csc open parentheses 90 degree close parentheses space end cell row blank equals cell negative open parentheses fraction numerator 1 over denominator sin open parentheses 90 degree close parentheses end fraction close parentheses squared minus cot open parentheses 90 degree close parentheses csc open parentheses 90 degree close parentheses end cell row blank equals cell negative open parentheses fraction numerator 1 over denominator sin open parentheses 90 degree close parentheses end fraction close parentheses squared minus cot open parentheses 90 degree close parentheses fraction numerator 1 over denominator sin open parentheses 90 degree close parentheses end fraction end cell row blank equals cell negative 1 over 1 squared minus 0 over 1 end cell row blank equals cell negative 1 end cell end table$

Jadi, f apostrophe open parentheses straight pi over 2 close parentheses equals negative 1 .