derivative of x^7ln(3x)

解

\frac{d}{d x} (x^{7} ln (3 x))

7 x^{6} ln (3 x) + x^{6}

解答ステップ

\frac{d}{d x} (x^{7} ln (3 x))

積の法則を適用:

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

f = x^{7}, g = ln (3 x)

= \frac{d}{d x} (x^{7}) ln (3 x) + \frac{d}{d x} (ln (3 x)) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 7 x^{6} ln (3 x) + \frac{1}{x} x^{7}

\frac{1}{x} x^{7} = x^{6}

= 7 x^{6} ln (3 x) + x^{6}