derivative of x^9ln(x)

解

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

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

\frac{1}{x} x^{9} = x^{8}

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