derivative 3arccos(x/2)

解

導関数

3 arccos (\frac{x}{2})

- \frac{3}{4 - x ^{2}}

解答ステップ

\frac{d}{d x} (3 arccos (\frac{x}{2}))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (arccos (\frac{x}{2}))

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{3}{4 - x ^{2}}