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Popular >

derivative of arctan(e^{-2x})

Solution

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

Solution

- \frac{2 e ^{- 2 x}}{e ^{- 4 x} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( e ^{- 2 x} ) ^{2} + 1} (- 2 e^{- 2 x}) : - \frac{2 e ^{- 2 x}}{e ^{- 4 x} + 1}

= - \frac{2 e ^{- 2 x}}{e ^{- 4 x} + 1}

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Frequently Asked Questions (FAQ)

What is the derivative of arctan(e^{-2x}) ?
The derivative of arctan(e^{-2x}) is -(2e^{-2x})/(e^{-4x)+1}
What is the first derivative of arctan(e^{-2x}) ?
The first derivative of arctan(e^{-2x}) is -(2e^{-2x})/(e^{-4x)+1}