derivative 3xarcsin(x)

解

導関数

3 x arcsin (x)

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

解答ステップ

\frac{d}{d x} (3 x arcsin (x))

定数を除去:

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

= 3 \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)

= 3 (\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}}

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

簡素化

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

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