What is the derivative of ((e^{-1-x}-e^{-1}))/x ?

The derivative of ((e^{-1-x}-e^{-1}))/x is (-e^{-x}x-e^{-x}+1)/(ex^2)

What is the first derivative of ((e^{-1-x}-e^{-1}))/x ?

The first derivative of ((e^{-1-x}-e^{-1}))/x is (-e^{-x}x-e^{-x}+1)/(ex^2)

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derivative of

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

\frac{- e ^{- x} x - e ^{- x} + 1}{e x ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{- 1 - x} - e ^{- 1}}{x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{- e ^{- x} x - e ^{- x} + 1}{e x ^{2}}

\int_{1}^{3} \frac{5}{x ^{2} + 2 x + 1} d x

f (x) = ln (5 - x)

\frac{d}{d x} (ln (x + y + 5))

\int \frac{1}{200 - x} d x

\frac{d y}{d t} + e^{t} y = - 18 e^{t}

What is the derivative of ((e^{-1-x}-e^{-1}))/x ?
The derivative of ((e^{-1-x}-e^{-1}))/x is (-e^{-x}x-e^{-x}+1)/(ex^2)
What is the first derivative of ((e^{-1-x}-e^{-1}))/x ?
The first derivative of ((e^{-1-x}-e^{-1}))/x is (-e^{-x}x-e^{-x}+1)/(ex^2)