derivative of 4x^2ln(x)

解

\frac{d}{d x} (4 x^{2} ln (x))

4 (2 x ln (x) + x)

解答ステップ

\frac{d}{d x} (4 x^{2} ln (x))

定数を除去:

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

= 4 \frac{d}{d x} (x^{2} ln (x))

積の法則を適用:

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

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

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

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

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

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

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

= 4 (2 x ln (x) + x)