derivative of arccos(2x^2)

解

\frac{d}{d x} (arccos (2 x^{2}))

- \frac{4 x}{1 - 4 x ^{4}}

解答ステップ

\frac{d}{d x} (arccos (2 x^{2}))

連鎖法則を適用:

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

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

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

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

簡素化

- \frac{1}{1 - ( 2 x ^{2} ) ^{2}} \cdot 4 x : - \frac{4 x}{1 - 4 x ^{4}}

= - \frac{4 x}{1 - 4 x ^{4}}