derivative y=6x^3ln(5x)

解

導関数

y = 6 x^{3} ln (5 x)

6 (3 x^{2} ln (5 x) + x^{2})

解答ステップ

\frac{d}{d x} (6 x^{3} ln (5 x))

定数を除去:

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

= 6 \frac{d}{d x} (x^{3} ln (5 x))

積の法則を適用:

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

f = x^{3}, g = ln (5 x)

= 6 (\frac{d}{d x} (x^{3}) ln (5 x) + \frac{d}{d x} (ln (5 x)) x^{3})

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

\frac{d}{d x} (ln (5 x)) = \frac{1}{x}

= 6 (3 x^{2} ln (5 x) + \frac{1}{x} x^{3})

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

= 6 (3 x^{2} ln (5 x) + x^{2})