derivative of a^xln(x)

解答

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

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

求解步骤

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

使用微分乘法定则:

(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}

11 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

d er i v a t i v e f (t) = 4 t^{2} - t

x \to 1 lim (x^{2} - x)

t an g e n t 9 x^{2} - x^{3}

\frac{d}{d x} (2 (π - e)^{4})