derivative x5^x

解答

导数

x 5^{x}

5^{x} + ln (5) \cdot 5^{x} x

求解步骤

\frac{d}{d x} (x \cdot 5^{x})

使用微分乘法定则:

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

f = x, g = 5^{x}

= \frac{d x}{d x} 5^{x} + \frac{d}{d x} (5^{x}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

= 1 \cdot 5^{x} + 5^{x} ln (5) x

化简

= 5^{x} + ln (5) \cdot 5^{x} x

t an g e n t \frac{2}{x}, at x = 3

\int \frac{2}{2 x + 1} d x

n = 1 \sum \infty 23 (\frac{2}{5})^{n}

\int \frac{e ^{x}}{3 - e ^{2 x}} d x

y (x + 3) + y^{^{'}} = 0