derivative 3sin(x)ln(x)

解

導関数

3 sin (x) ln (x)

3 (cos (x) ln (x) + \frac{sin ( x )}{x})

解答ステップ

\frac{d}{d x} (3 sin (x) ln (x))

定数を除去:

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

= 3 \frac{d}{d x} (sin (x) ln (x))

積の法則を適用:

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

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

= 3 (\frac{d}{d x} (sin (x)) ln (x) + \frac{d}{d x} (ln (x)) sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

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

= 3 (cos (x) ln (x) + \frac{1}{x} sin (x))

\frac{1}{x} sin (x) = \frac{sin ( x )}{x}

= 3 (cos (x) ln (x) + \frac{sin ( x )}{x})