derivative-(x+3arcsin(x))/4

解

導関数

- \frac{x + 3 arcsin ( x )}{4}

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

解答ステップ

\frac{d}{d x} (- \frac{x + 3 arcsin ( x )}{4})

定数を除去:

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

= - \frac{1}{4} \frac{d}{d x} (x + 3 arcsin (x))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{1}{4} (\frac{d x}{d x} + \frac{d}{d x} (3 arcsin (x)))

\frac{d x}{d x} = 1

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

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