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

解答

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

\frac{- e ^{x} x + 6 e ^{x}}{( 5 - x ) ^{2}}

求解步骤

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

使用微分除法定则:

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

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

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

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

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

化简

\frac{e ^{x} ( 5 - x ) - ( - 1 ) e ^{x}}{( 5 - x ) ^{2}} : \frac{- e ^{x} x + 6 e ^{x}}{( 5 - x ) ^{2}}

= \frac{- e ^{x} x + 6 e ^{x}}{( 5 - x ) ^{2}}

d er i v a t i v e f (x) = ln (ln (x^{3} e^{- 3 x}))

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

\frac{d ^{2}}{d x ^{2}} (\frac{3 x + 5}{2 x - 1})

y^{^{'}} + x y = x y^{- 2}

\frac{d}{d x} (12 x - 3 x^{2})