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Popular >

derivative of ln(x-e^{-x})

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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