derivative y=ln(x)sqrt(x)

解

導関数

y = ln (x) x

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

解答ステップ

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

積の法則を適用:

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

f = ln (x), g = x

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

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

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

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

簡素化

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

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