derivative 4sqrt(x)ln(x)

解

導関数

4 x ln (x)

4 (\frac{ln ( x )}{2 x} + \frac{1}{x})

解答ステップ

\frac{d}{d x} (4 x ln (x))

定数を除去:

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

= 4 \frac{d}{d x} (x ln (x))

積の法則を適用:

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

f = x, g = ln (x)

= 4 (\frac{d}{d x} (x) ln (x) + \frac{d}{d x} (ln (x)) x)

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= 4 (\frac{1}{2 x} ln (x) + \frac{1}{x} x)

簡素化

4 (\frac{1}{2 x} ln (x) + \frac{1}{x} x) : 4 (\frac{ln ( x )}{2 x} + \frac{1}{x})

= 4 (\frac{ln ( x )}{2 x} + \frac{1}{x})