derivative of 3^xln(x)

解答

\frac{d}{d x} (3^{x} ln (x))

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

求解步骤

\frac{d}{d x} (3^{x} ln (x))

使用微分乘法定则:

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

f = 3^{x}, g = ln (x)

= \frac{d}{d x} (3^{x}) ln (x) + \frac{d}{d x} (ln (x)) 3^{x}

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

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

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

\frac{1}{x} \cdot 3^{x} = \frac{3 ^{x}}{x}

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

\int \frac{4 x ^{2} - 25}{x ^{3}} d x

\frac{d}{d x} (3 e^{x} + (x - 2)^{2})

x \to 6 lim (5)

y^{^{''}} + 10 y^{^{'}} + 25 y = 7 e^{2 x}

\int_{- \infty}^{3} x e^{x} d x