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

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

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

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

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derivative of

y = 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}}

(2 x^{3} + 5 x) (x - 3) (x + 2)

\frac{d}{d x} (ln (y - x))

- x^{2} + 8 x - 9, (\frac{1}{2} x) + 1, x = 3, x = 5

\int_{- \infty}^{0} \frac{1}{7 - 5 x} d x

\int x^{2} (1 - x^{3})^{5} d x

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