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Popular >

derivative of 3e^{-x/4}

Solution

\frac{d}{d x} (3 e^{- \frac{x}{4}})

Solution

- \frac{3}{4} e^{- \frac{x}{4}}

Solution steps

\frac{d}{d x} (3 e^{- \frac{x}{4}})

Take the constant out:

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

= 3 \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}

= 3 e^{- \frac{x}{4}} (- \frac{1}{4})

Simplify

3 e^{- \frac{x}{4}} (- \frac{1}{4}) : - \frac{3}{4} e^{- \frac{x}{4}}

= - \frac{3}{4} e^{- \frac{x}{4}}

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Frequently Asked Questions (FAQ)

What is the derivative of 3e^{-x/4} ?
The derivative of 3e^{-x/4} is -3/4 e^{-x/4}
What is the first derivative of 3e^{-x/4} ?
The first derivative of 3e^{-x/4} is -3/4 e^{-x/4}