What is the derivative of 1/4 e^{-x/2} ?

The derivative of 1/4 e^{-x/2} is -1/8 e^{-x/2}

What is the first derivative of 1/4 e^{-x/2} ?

The first derivative of 1/4 e^{-x/2} is -1/8 e^{-x/2}

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

- \frac{1}{8} e^{- \frac{x}{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \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}

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

Simplify

\frac{1}{4} e^{- \frac{x}{2}} (- \frac{1}{2}) : - \frac{1}{8} e^{- \frac{x}{2}}

= - \frac{1}{8} e^{- \frac{x}{2}}

What is the derivative of 1/4 e^{-x/2} ?
The derivative of 1/4 e^{-x/2} is -1/8 e^{-x/2}
What is the first derivative of 1/4 e^{-x/2} ?
The first derivative of 1/4 e^{-x/2} is -1/8 e^{-x/2}