Pertanyaan

Tentukan turunan pertama dari setiap fungsi berikut ini dengan teliti. b. y = ( tan x × sec x ) 3

Tentukan turunan pertama dari setiap fungsi berikut ini dengan teliti.

b. $y = (tan x \times sec x)^{3}$

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Jawaban terverifikasi

Jawaban

turunan dari adalah .

turunan dari y equals open parentheses tan x space cross times space s e c x close parentheses cubed

adalah

y apostrophe equals 3 sec to the power of 5 open parentheses x close parentheses tan squared open parentheses x close parentheses plus 3 tan to the power of 4 open parentheses x close parentheses sec cubed open parentheses x close parentheses

Pembahasan

Cari turunan Ingat aturan berikut, Maka, Cari turunan Kemudian cari turunan Maka, Jadi, turunan dari adalah .

open parentheses tan open parentheses x close parentheses sec open parentheses x close parentheses close parentheses cubed equals tan cubed open parentheses x close parentheses sec cubed open parentheses x close parentheses

Cari turunan $fraction numerator d over denominator d x end fraction open parentheses tan cubed open parentheses x close parentheses sec cubed open parentheses x close parentheses close parentheses$

Ingat aturan berikut,

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f times g close parentheses apostrophe end cell equals cell f thin space apostrophe times g plus f times g apostrophe end cell row f equals cell tan cubed open parentheses x close parentheses end cell row g equals cell sec cubed open parentheses x close parentheses end cell end table

Maka,

$begin mathsize 12px style fraction numerator d over denominator d x end fraction open parentheses tan cubed open parentheses x close parentheses sec cubed open parentheses x close parentheses close parentheses equals fraction numerator d over denominator d x end fraction open parentheses tan cubed open parentheses x close parentheses close parentheses sec cubed open parentheses x close parentheses plus fraction numerator d over denominator d x end fraction open parentheses sec cubed open parentheses x close parentheses close parentheses tan cubed open parentheses x close parentheses end style$

Cari turunan $fraction numerator d over denominator d x end fraction open parentheses tan cubed open parentheses x close parentheses close parentheses$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction end cell equals cell fraction numerator d f over denominator d u end fraction fraction numerator d u over denominator d x end fraction end cell row f equals cell u cubed end cell row u equals cell tan open parentheses x close parentheses end cell row cell fraction numerator d over denominator d x end fraction open parentheses tan cubed open parentheses x close parentheses close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses u cubed close parentheses fraction numerator d over denominator d x end fraction open parentheses tan open parentheses x close parentheses close parentheses end cell row blank equals cell 3 u to the power of 3 minus 1 end exponent fraction numerator d over denominator d x end fraction open parentheses tan open parentheses x close parentheses close parentheses end cell row blank equals cell 3 u squared fraction numerator d over denominator d x end fraction open parentheses tan open parentheses x close parentheses close parentheses end cell row blank equals cell 3 open parentheses tan open parentheses x close parentheses close parentheses squared fraction numerator d over denominator d x end fraction open parentheses tan open parentheses x close parentheses close parentheses end cell row blank equals cell 3 open parentheses tan open parentheses x close parentheses close parentheses squared sec squared open parentheses x close parentheses end cell end table$

Kemudian cari turunan $fraction numerator d over denominator d x end fraction open parentheses sec cubed open parentheses x close parentheses close parentheses$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction end cell equals cell fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row cell fraction numerator d over denominator d x end fraction open parentheses sec cubed open parentheses x close parentheses close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses u cubed close parentheses fraction numerator d over denominator d x end fraction open parentheses sec open parentheses x close parentheses close parentheses end cell row blank equals cell 3 u to the power of 3 minus 1 end exponent fraction numerator d over denominator d x end fraction open parentheses sec open parentheses x close parentheses close parentheses end cell row blank equals cell 3 u squared fraction numerator d over denominator d x end fraction open parentheses sec open parentheses x close parentheses close parentheses end cell row blank equals cell 3 open parentheses sec open parentheses x close parentheses close parentheses squared fraction numerator d over denominator d x end fraction open parentheses sec open parentheses x close parentheses close parentheses end cell row blank equals cell 3 open parentheses sec open parentheses x close parentheses close parentheses squared sec open parentheses x close parentheses tan open parentheses x close parentheses end cell row blank equals cell 3 sec to the power of 2 plus 1 end exponent open parentheses x close parentheses tan open parentheses x close parentheses end cell row blank equals cell 3 sec cubed open parentheses x close parentheses tan open parentheses x close parentheses end cell end table$

Maka,

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses tan cubed open parentheses x close parentheses sec cubed open parentheses x close parentheses close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses tan cubed open parentheses x close parentheses close parentheses sec cubed open parentheses x close parentheses plus fraction numerator d over denominator d x end fraction open parentheses sec cubed open parentheses x close parentheses close parentheses tan cubed open parentheses x close parentheses end cell row blank equals cell 3 tan squared open parentheses x close parentheses sec squared open parentheses x close parentheses sec cubed open parentheses x close parentheses plus 3 sec cubed open parentheses x close parentheses tan open parentheses x close parentheses tan cubed open parentheses x close parentheses end cell row blank equals cell 3 tan squared open parentheses x close parentheses sec to the power of 2 plus 3 end exponent open parentheses x close parentheses plus 3 sec cubed open parentheses x close parentheses tan to the power of 1 plus 3 end exponent open parentheses x close parentheses end cell row blank equals cell 3 tan squared open parentheses x close parentheses sec to the power of 5 open parentheses x close parentheses plus 3 sec cubed open parentheses x close parentheses tan to the power of 4 open parentheses x close parentheses end cell row blank equals cell 3 sec to the power of 5 open parentheses x close parentheses tan squared open parentheses x close parentheses plus 3 tan to the power of 4 open parentheses x close parentheses sec cubed open parentheses x close parentheses end cell end table end style$

Jadi, turunan dari y equals open parentheses tan x space cross times space s e c x close parentheses cubed adalah y apostrophe equals 3 sec to the power of 5 open parentheses x close parentheses tan squared open parentheses x close parentheses plus 3 tan to the power of 4 open parentheses x close parentheses sec cubed open parentheses x close parentheses .