derivative xsqrt(ln(x))

解

導関数

x ln (x)

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

解答ステップ

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

積の法則を適用:

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

f = x, g = ln (x)

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

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

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

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

簡素化

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

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