derivative of x^8ln(9x)

解

\frac{d}{d x} (x^{8} ln (9 x))

8 x^{7} ln (9 x) + x^{7}

解答ステップ

\frac{d}{d x} (x^{8} ln (9 x))

積の法則を適用:

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

f = x^{8}, g = ln (9 x)

= \frac{d}{d x} (x^{8}) ln (9 x) + \frac{d}{d x} (ln (9 x)) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} (ln (9 x)) = \frac{1}{x}

= 8 x^{7} ln (9 x) + \frac{1}{x} x^{8}

\frac{1}{x} x^{8} = x^{7}

= 8 x^{7} ln (9 x) + x^{7}