derivative arccos(7x^3)

解

導関数

arccos (7 x^{3})

- \frac{21 x ^{2}}{1 - 49 x ^{6}}

解答ステップ

\frac{d}{d x} (arccos (7 x^{3}))

連鎖法則を適用:

- \frac{1}{1 - ( 7 x ^{3} ) ^{2}} \frac{d}{d x} (7 x^{3})

= - \frac{1}{1 - ( 7 x ^{3} ) ^{2}} \frac{d}{d x} (7 x^{3})

\frac{d}{d x} (7 x^{3}) = 21 x^{2}

= - \frac{1}{1 - ( 7 x ^{3} ) ^{2}} \cdot 21 x^{2}

簡素化

- \frac{1}{1 - ( 7 x ^{3} ) ^{2}} \cdot 21 x^{2} : - \frac{21 x ^{2}}{1 - 49 x ^{6}}

= - \frac{21 x ^{2}}{1 - 49 x ^{6}}