derivative y=xarcsin(2x)

解

導関数

y = x arcsin (2 x)

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

解答ステップ

\frac{d}{d x} (x arcsin (2 x))

積の法則を適用:

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

f = x, g = arcsin (2 x)

= \frac{d x}{d x} arcsin (2 x) + \frac{d}{d x} (arcsin (2 x)) x

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

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

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

簡素化

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

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