derivative x*arcsin(sqrt(x))

解

導関数

x \cdot arcsin (x)

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

解答ステップ

\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{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}{2 x 1 - x}

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

簡素化

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

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