derivative of sqrt(x)ln(10x)

解

\frac{d}{d x} (x ln (10 x))

\frac{ln ( 10 x )}{2 x} + \frac{1}{x}

解答ステップ

\frac{d}{d x} (x ln (10 x))

積の法則を適用:

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

f = x, g = ln (10 x)

= \frac{d}{d x} (x) ln (10 x) + \frac{d}{d x} (ln (10 x)) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (ln (10 x)) = \frac{1}{x}

= \frac{1}{2 x} ln (10 x) + \frac{1}{x} x

簡素化

\frac{1}{2 x} ln (10 x) + \frac{1}{x} x : \frac{ln ( 10 x )}{2 x} + \frac{1}{x}

= \frac{ln ( 10 x )}{2 x} + \frac{1}{x}