derivative of e^x(x-3)

解答

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

e^{x} x - 2 e^{x}

求解步骤

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

使用微分乘法定则:

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

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

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

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

\frac{d}{d x} (x - 3) = 1

= e^{x} (x - 3) + 1 \cdot e^{x}

化简

e^{x} (x - 3) + 1 \cdot e^{x} : e^{x} x - 2 e^{x}

= e^{x} x - 2 e^{x}

a re a x, \frac{1}{2} x, 9

x \to - 1 + lim (2 x^{3} - 2 m)

d er i v a t i v e f (x) = 5 e^{2 x}

\frac{d y}{d x} = \frac{e ^{x}}{8 + e ^{x}}

\frac{d}{d x} (e^{6 x^{2}})