derivative of 9^xln(x)

解

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

2 ln (3) \cdot 9^{x} ln (x) + \frac{9 ^{x}}{x}

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (9^{x}) = 2 ln (3) \cdot 9^{x}

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

= 2 ln (3) \cdot 9^{x} ln (x) + \frac{1}{x} \cdot 9^{x}

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

= 2 ln (3) \cdot 9^{x} ln (x) + \frac{9 ^{x}}{x}