derivative e^x*x

解答

导数

e^{x} \cdot x

e^{x} x + e^{x}

求解步骤

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

使用微分乘法定则:

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

f = e^{x}, g = x

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

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

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

= e^{x} x + 1 \cdot e^{x}

化简

= e^{x} x + e^{x}

d er i v a t i v e f (x) = - \frac{12 x}{( x ^{2} + 2 ) ^{\frac{5}{2}}}

n = 1 \sum \infty \frac{1}{n !}

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