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Popular >

derivative of e^{(-x/4})

Solution

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

Solution

- \frac{1}{4} e^{- \frac{x}{4}}

Solution steps

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

Simplify

e^{\frac{- x}{4}} : e^{- \frac{x}{4}}

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

Apply the chain rule:

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

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

\frac{d}{d x} (- \frac{x}{4}) = - \frac{1}{4}

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

Simplify

= - \frac{1}{4} e^{- \frac{x}{4}}

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Frequently Asked Questions (FAQ)

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