derivative of arccos(4x^3)

解

\frac{d}{d x} (arccos (4 x^{3}))

- \frac{12 x ^{2}}{1 - 16 x ^{6}}

解答ステップ

\frac{d}{d x} (arccos (4 x^{3}))

連鎖法則を適用:

- \frac{1}{1 - ( 4 x ^{3} ) ^{2}} \frac{d}{d x} (4 x^{3})

= - \frac{1}{1 - ( 4 x ^{3} ) ^{2}} \frac{d}{d x} (4 x^{3})

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

= - \frac{1}{1 - ( 4 x ^{3} ) ^{2}} \cdot 12 x^{2}

簡素化

- \frac{1}{1 - ( 4 x ^{3} ) ^{2}} \cdot 12 x^{2} : - \frac{12 x ^{2}}{1 - 16 x ^{6}}

= - \frac{12 x ^{2}}{1 - 16 x ^{6}}