derivative y=4x^3ln(x)

解

導関数

y = 4 x^{3} ln (x)

4 (3 x^{2} ln (x) + x^{2})

解答ステップ

\frac{d}{d x} (4 x^{3} ln (x))

定数を除去:

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

= 4 \frac{d}{d x} (x^{3} ln (x))

積の法則を適用:

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

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

= 4 (\frac{d}{d x} (x^{3}) ln (x) + \frac{d}{d x} (ln (x)) x^{3})

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

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

= 4 (3 x^{2} ln (x) + \frac{1}{x} x^{3})

\frac{1}{x} x^{3} = x^{2}

= 4 (3 x^{2} ln (x) + x^{2})