derivative of x^6ln(7x)

解

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

6 x^{5} ln (7 x) + x^{5}

解答ステップ

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

積の法則を適用:

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

f = x^{6}, g = ln (7 x)

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

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

\frac{d}{d x} (ln (7 x)) = \frac{1}{x}

= 6 x^{5} ln (7 x) + \frac{1}{x} x^{6}

\frac{1}{x} x^{6} = x^{5}

= 6 x^{5} ln (7 x) + x^{5}