derivative of (x-5/(4x^2e^x))

解答

\frac{d}{d x} (\frac{x - 5}{4 x ^{2} e ^{x}})

\frac{- x ^{2} + 4 x + 10}{4 e ^{x} x ^{3}}

求解步骤

\frac{d}{d x} (\frac{x - 5}{4 x ^{2} e ^{x}})

将常数提出:

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

= \frac{1}{4} \frac{d}{d x} (\frac{x - 5}{x ^{2} e ^{x}})

使用微分除法定则:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( x - 5 ) x ^{2} e ^{x} - \frac{d}{d x} ( x ^{2} e ^{x} ) ( x - 5 )}{( x ^{2} e ^{x} ) ^{2}}

\frac{d}{d x} (x - 5) = 1

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

= \frac{1}{4} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x - 5 )}{( x ^{2} e ^{x} ) ^{2}}

化简

\frac{1}{4} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x - 5 )}{( x ^{2} e ^{x} ) ^{2}} : \frac{- x ^{2} + 4 x + 10}{4 e ^{x} x ^{3}}

= \frac{- x ^{2} + 4 x + 10}{4 e ^{x} x ^{3}}

x \to 0 lim (x^{4} cos (\frac{1}{x}))

(e^{- 2 t})^{^{'}}

\int \frac{- 6 x ^{4} + 6}{x ^{2} + 1} d x

\int \frac{1}{e ^{10 x}} d x

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