derivative of (x^2+2xln(2x))

解

\frac{d}{d x} ((x^{2} + 2 x) ln (2 x))

ln (2 x) (2 x + 2) + x + 2

解答ステップ

\frac{d}{d x} ((x^{2} + 2 x) ln (2 x))

積の法則を適用:

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

f = x^{2} + 2 x, g = ln (2 x)

= \frac{d}{d x} (x^{2} + 2 x) ln (2 x) + \frac{d}{d x} (ln (2 x)) (x^{2} + 2 x)

\frac{d}{d x} (x^{2} + 2 x) = 2 x + 2

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

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

\frac{1}{x} (x^{2} + 2 x) = x + 2

= ln (2 x) (2 x + 2) + x + 2