derivative f(x)=sqrt(3x)ln(19x)

解

導関数

f (x) = 3 x ln (19 x)

\frac{3 ln ( 19 x )}{2 x} + \frac{3}{x}

解答ステップ

\frac{d}{d x} (3 x ln (19 x))

積の法則を適用:

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

f = 3 x, g = ln (19 x)

= \frac{d}{d x} (3 x) ln (19 x) + \frac{d}{d x} (ln (19 x)) 3 x

\frac{d}{d x} (3 x) = \frac{3}{2 x}

\frac{d}{d x} (ln (19 x)) = \frac{1}{x}

= \frac{3}{2 x} ln (19 x) + \frac{1}{x} 3 x

簡素化

\frac{3}{2 x} ln (19 x) + \frac{1}{x} 3 x : \frac{3 ln ( 19 x )}{2 x} + \frac{3}{x}

= \frac{3 ln ( 19 x )}{2 x} + \frac{3}{x}