derivative y=(e^x)/(5x^2)

解答

导数

y = \frac{e ^{x}}{5 x ^{2}}

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

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{5} \frac{d}{d x} (\frac{e ^{x}}{x ^{2}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( e ^{x} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) e ^{x}}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{5} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}}

化简

\frac{1}{5} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}} : \frac{e ^{x} ( x - 2 )}{5 x ^{3}}

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

\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))

y^{^{'}} = y^{2} e^{2 x}

d er i v a t i v e ln (\frac{2 + x}{1 + x})