derivative f(x)=(x+2sqrt(x))e^x

解答

导数

f (x) = (x + 2 x) e^{x}

(1 + \frac{1}{x}) e^{x} + e^{x} (x + 2 x)

求解步骤

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

使用微分乘法定则:

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

f = x + 2 x, g = e^{x}

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

\frac{d}{d x} (x + 2 x) = 1 + \frac{1}{x}

\frac{d}{d x} (e^{x}) = e^{x}

= (1 + \frac{1}{x}) e^{x} + e^{x} (x + 2 x)

\int \frac{13}{13 + e ^{x}} d x

\frac{d y}{d x} = 6 - 3 x^{2}

\int e^{x} \cdot x^{- 1} d x

\frac{d y}{d x} = \frac{4 y ln ( x )}{x}

\int_{\frac{π}{2}}^{π} 2 cot (\frac{x}{2}) d x