derivative sec(\sqrt[3]{x^5-2})

解

導関数

sec (3 x^{5} - 2)

\frac{5 x ^{4} sec ( 3 x ^{5} - 2 ) tan ( 3 x ^{5} - 2 )}{3 ( x ^{5} - 2 ) ^{\frac{2}{3}}}

解答ステップ

\frac{d}{d x} (sec (3 x^{5} - 2))

連鎖法則を適用:

sec (3 x^{5} - 2) tan (3 x^{5} - 2) \frac{d}{d x} (3 x^{5} - 2)

= sec (3 x^{5} - 2) tan (3 x^{5} - 2) \frac{d}{d x} (3 x^{5} - 2)

\frac{d}{d x} (3 x^{5} - 2) = \frac{5 x ^{4}}{3 ( x ^{5} - 2 ) ^{\frac{2}{3}}}

= sec (3 x^{5} - 2) tan (3 x^{5} - 2) \frac{5 x ^{4}}{3 ( x ^{5} - 2 ) ^{\frac{2}{3}}}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 x ^{4} sec ( 3 x ^{5} - 2 ) tan ( 3 x ^{5} - 2 )}{3 ( x ^{5} - 2 ) ^{\frac{2}{3}}}