derivative y=arccos(sqrt(x))

解

導関数

y = arccos (x)

- \frac{1}{2 x 1 - x}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{1}{2 x 1 - x}