derivative of a{r}(xc,(ln(x)))

解

\frac{d}{d x} (a r (x) c, (ln (x)))

(a c, (\frac{d}{d x} (r (x)) ln (x) + \frac{1}{x} r (x)))

解答ステップ

\frac{d}{d x} (a r (x) c, (ln (x)))

定数を除去:

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

= (a c, \frac{d}{d x} (r (x) ln (x)))

積の法則を適用:

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

f = r (x), g = ln (x)

= (a c, (\frac{d}{d x} (r (x)) ln (x) + \frac{d}{d x} (ln (x)) r (x)))

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

= (a c, (\frac{d}{d x} (r (x)) ln (x) + \frac{1}{x} r (x)))