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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (- 3 e^{3 y} sin (3 x))

x = y^{2}, x = y + 2 [0, 4]

\frac{d}{d x} (x^{5} + x^{7} + x^{9})

x \to + 2 lim (3 x - 9)

\int x^{2} + 4 x + 13 d x

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