What is the derivative of 30e^{-(x^2/3}) ?

The derivative of 30e^{-(x^2/3}) is -20e^{-(x^2)/3}x

What is the first derivative of 30e^{-(x^2/3}) ?

The first derivative of 30e^{-(x^2/3}) is -20e^{-(x^2)/3}x

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\frac{d}{d x} (30 e^{- \frac{x ^{2}}{3}})

- 20 e^{- \frac{x ^{2}}{3}} x

Solution steps

\frac{d}{d x} (30 e^{- \frac{x ^{2}}{3}})

Take the constant out:

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

= 30 \frac{d}{d x} (e^{- \frac{x ^{2}}{3}})

Apply the chain rule:

e^{- \frac{x ^{2}}{3}} \frac{d}{d x} (- \frac{x ^{2}}{3})

= e^{- \frac{x ^{2}}{3}} \frac{d}{d x} (- \frac{x ^{2}}{3})

\frac{d}{d x} (- \frac{x ^{2}}{3}) = - \frac{2 x}{3}

= 30 e^{- \frac{x ^{2}}{3}} (- \frac{2 x}{3})

Simplify

30 e^{- \frac{x ^{2}}{3}} (- \frac{2 x}{3}) : - 20 e^{- \frac{x ^{2}}{3}} x

= - 20 e^{- \frac{x ^{2}}{3}} x

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What is the derivative of 30e^{-(x^2/3}) ?
The derivative of 30e^{-(x^2/3}) is -20e^{-(x^2)/3}x
What is the first derivative of 30e^{-(x^2/3}) ?
The first derivative of 30e^{-(x^2/3}) is -20e^{-(x^2)/3}x