What is the derivative of e^{-1/2 x} ?

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

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

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

Popular >

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{3 e ^{- 7 s}}{s ^{2}} + \frac{7 e ^{- 7 s}}{s} + \frac{2 e ^{- 7 s}}{s}

\int 2 x e^{- 2 x} d x

\frac{d}{d x} (\frac{x ^{3} + 5}{x ^{2} + 2 x + 3})

f (x) = x^{3}

\int lo g_{6} (x) d x

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