derivative (7x^2-11x)e^x

解答

导数

(7 x^{2} - 11 x) e^{x}

7 e^{x} x^{2} + 3 e^{x} x - 11 e^{x}

求解步骤

\frac{d}{d x} ((7 x^{2} - 11 x) e^{x})

使用微分乘法定则:

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

f = 7 x^{2} - 11 x, g = e^{x}

= \frac{d}{d x} (7 x^{2} - 11 x) e^{x} + \frac{d}{d x} (e^{x}) (7 x^{2} - 11 x)

\frac{d}{d x} (7 x^{2} - 11 x) = 14 x - 11

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

= (14 x - 11) e^{x} + e^{x} (7 x^{2} - 11 x)

化简

(14 x - 11) e^{x} + e^{x} (7 x^{2} - 11 x) : 7 e^{x} x^{2} + 3 e^{x} x - 11 e^{x}

= 7 e^{x} x^{2} + 3 e^{x} x - 11 e^{x}

d er i v a t i v e f (x) = \frac{1}{5 x}

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

t an g e n t f (x) = x^{3} - 4 x^{2}, at x = 0

d er i v a t i v e ln (\frac{3 + e ^{x}}{3 - e ^{x}})

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