Pertanyaan

Tentukan turunan pertama fungsi trigonometri berikut dengan kritis dan analitis. b. y = co t − 1 ( sin x )

Tentukan turunan pertama fungsi trigonometri berikut dengan kritis dan analitis.

b. $y = co t^{- 1} (sin x)$

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

turunan adalah .

turunan

y equals co t to the power of negative 1 end exponent left parenthesis sin x right parenthesis

adalah $negative fraction numerator cos open parentheses x close parentheses over denominator sin squared open parentheses x close parentheses plus 1 end fraction$ .

Pembahasan

Ingatlah! Cari turunan Jadi, turunan adalah .

Ingatlah!

cot to the power of negative 1 end exponent equals arccot

Cari turunan y equals co t to the power of negative 1 end exponent left parenthesis sin x right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction end cell equals cell fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row f equals cell a r c c o t left parenthesis u right parenthesis end cell row u equals cell sin left parenthesis x right parenthesis end cell row cell fraction numerator d over denominator d x end fraction open parentheses arccot open parentheses sin open parentheses x close parentheses close parentheses close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses arccot open parentheses u close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator 1 over denominator u squared plus 1 end fraction fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator 1 over denominator open parentheses sin open parentheses x close parentheses close parentheses squared plus 1 end fraction cos open parentheses x close parentheses end cell row blank equals cell negative fraction numerator 1 times cos open parentheses x close parentheses over denominator sin squared open parentheses x close parentheses plus 1 end fraction end cell row blank equals cell negative fraction numerator cos open parentheses x close parentheses over denominator sin squared open parentheses x close parentheses plus 1 end fraction end cell row blank equals cell negative fraction numerator cos open parentheses x close parentheses over denominator sin squared open parentheses x close parentheses plus 1 end fraction end cell end table$

Jadi, turunan y equals co t to the power of negative 1 end exponent left parenthesis sin x right parenthesis adalah $negative fraction numerator cos open parentheses x close parentheses over denominator sin squared open parentheses x close parentheses plus 1 end fraction$ .