derivative sin(x)ln(8x)

解

導関数

sin (x) ln (8 x)

cos (x) ln (8 x) + \frac{sin ( x )}{x}

解答ステップ

\frac{d}{d x} (sin (x) ln (8 x))

積の法則を適用:

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

f = sin (x), g = ln (8 x)

= \frac{d}{d x} (sin (x)) ln (8 x) + \frac{d}{d x} (ln (8 x)) sin (x)

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

\frac{d}{d x} (ln (8 x)) = \frac{1}{x}

= cos (x) ln (8 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (8 x) + \frac{sin ( x )}{x}