derivative of cxln(x)

解

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

c (ln (x) + 1)

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= c \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)

= c (\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}{x}

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

簡素化

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

= c (ln (x) + 1)