derivative of (3x^2-5xe^x)

解答

\frac{d}{d x} ((3 x^{2} - 5 x) e^{x})

3 e^{x} x^{2} + e^{x} x - 5 e^{x}

求解步骤

\frac{d}{d x} ((3 x^{2} - 5 x) e^{x})

使用微分乘法定则:

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

f = 3 x^{2} - 5 x, g = e^{x}

= \frac{d}{d x} (3 x^{2} - 5 x) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} - 5 x)

\frac{d}{d x} (3 x^{2} - 5 x) = 6 x - 5

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

= (6 x - 5) e^{x} + e^{x} (3 x^{2} - 5 x)

化简

(6 x - 5) e^{x} + e^{x} (3 x^{2} - 5 x) : 3 e^{x} x^{2} + e^{x} x - 5 e^{x}

= 3 e^{x} x^{2} + e^{x} x - 5 e^{x}

\int \frac{x}{x - 1} d x

d er i v a t i v e y = \frac{e ^{x}}{5 x ^{2}}

\frac{d}{d x} ((2 x + 3)^{1.4})

\frac{\partial}{\partial x} (x + y^{\frac{1}{2}})

x \to 0 lim (tan (7 x))