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Popular >

derivative of sqrt(1+e^{-5x)}

Solution

\frac{d}{d x} (1 + e^{- 5 x})

Solution

- \frac{5 e ^{- 5 x}}{2 1 + e ^{- 5 x}}

Solution steps

\frac{d}{d x} (1 + e^{- 5 x})

Apply the chain rule:

\frac{1}{2 1 + e ^{- 5 x}} \frac{d}{d x} (1 + e^{- 5 x})

= \frac{1}{2 1 + e ^{- 5 x}} \frac{d}{d x} (1 + e^{- 5 x})

\frac{d}{d x} (1 + e^{- 5 x}) = - 5 e^{- 5 x}

= \frac{1}{2 1 + e ^{- 5 x}} (- 5 e^{- 5 x})

Simplify

\frac{1}{2 1 + e ^{- 5 x}} (- 5 e^{- 5 x}) : - \frac{5 e ^{- 5 x}}{2 1 + e ^{- 5 x}}

= - \frac{5 e ^{- 5 x}}{2 1 + e ^{- 5 x}}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(1+e^{-5x)} ?
The derivative of sqrt(1+e^{-5x)} is -(5e^{-5x})/(2sqrt(1+e^{-5x))}
What is the first derivative of sqrt(1+e^{-5x)} ?
The first derivative of sqrt(1+e^{-5x)} is -(5e^{-5x})/(2sqrt(1+e^{-5x))}