derivative y=x^2ln(3x)

解

derivative

2 x ln (3 x) + x

解答ステップ

\frac{d}{d x} (x^{2} ln (3 x))

積の法則を適用:

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

f = x^{2}, g = ln (3 x)

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

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

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

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

\frac{1}{x} x^{2} = x

= 2 x ln (3 x) + x