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Popular Calculus >

derivative of arcsin(e^{-x})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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