derivative sqrt(15x)ln(14x)

解

導関数

15 x ln (14 x)

\frac{15 ln ( 14 x )}{2 x} + \frac{15}{x}

解答ステップ

\frac{d}{d x} (15 x ln (14 x))

積の法則を適用:

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

f = 15 x, g = ln (14 x)

= \frac{d}{d x} (15 x) ln (14 x) + \frac{d}{d x} (ln (14 x)) 15 x

\frac{d}{d x} (15 x) = \frac{15}{2 x}

\frac{d}{d x} (ln (14 x)) = \frac{1}{x}

= \frac{15}{2 x} ln (14 x) + \frac{1}{x} 15 x

簡素化

\frac{15}{2 x} ln (14 x) + \frac{1}{x} 15 x : \frac{15 ln ( 14 x )}{2 x} + \frac{15}{x}

= \frac{15 ln ( 14 x )}{2 x} + \frac{15}{x}