What is the derivative of (e^{-x}/(2-x)) ?

The derivative of (e^{-x}/(2-x)) is (e^{-x}x-e^{-x})/((2-x)^2)

What is the first derivative of (e^{-x}/(2-x)) ?

The first derivative of (e^{-x}/(2-x)) is (e^{-x}x-e^{-x})/((2-x)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (2 - x) = - 1

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

Simplify

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

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

\frac{d}{d x} (168 (2 x + 5)^{5})

\frac{d}{d x} ((\frac{x + 1}{x - 1})^{7})

\frac{\partial}{\partial x} (ln (x y^{2} z^{3}))

\frac{d}{d x} (7 cos (3 x))

y (θ) = 4 sin (θ) - 3 cos (θ)

What is the derivative of (e^{-x}/(2-x)) ?
The derivative of (e^{-x}/(2-x)) is (e^{-x}x-e^{-x})/((2-x)^2)
What is the first derivative of (e^{-x}/(2-x)) ?
The first derivative of (e^{-x}/(2-x)) is (e^{-x}x-e^{-x})/((2-x)^2)