derivative x/4 arcsin(x)

解

導関数

\frac{x}{4} arcsin (x)

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

解答ステップ

\frac{d}{d x} (\frac{x}{4} arcsin (x))

定数を除去:

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

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arcsin (x)

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

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

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

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

簡素化

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

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