derivative of a^xln(x)

解

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

a^{x} ln (a) ln (x) + \frac{a ^{x}}{x}

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

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

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

\frac{1}{x} a^{x} = \frac{a ^{x}}{x}

= a^{x} ln (a) ln (x) + \frac{a ^{x}}{x}