What is the derivative of-4e^{-5x^2} ?

The derivative of-4e^{-5x^2} is 40e^{-5x^2}x

What is the first derivative of-4e^{-5x^2} ?

The first derivative of-4e^{-5x^2} is 40e^{-5x^2}x

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derivative of

- 4 e^{- 5 x^{2}}

40 e^{- 5 x^{2}} x

Solution steps

\frac{d}{d x} (- 4 e^{- 5 x^{2}})

Take the constant out:

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

= - 4 \frac{d}{d x} (e^{- 5 x^{2}})

Apply the chain rule:

e^{- 5 x^{2}} \frac{d}{d x} (- 5 x^{2})

= e^{- 5 x^{2}} \frac{d}{d x} (- 5 x^{2})

\frac{d}{d x} (- 5 x^{2}) = - 10 x

= - 4 e^{- 5 x^{2}} (- 10 x)

Simplify

= 40 e^{- 5 x^{2}} x

What is the derivative of-4e^{-5x^2} ?
The derivative of-4e^{-5x^2} is 40e^{-5x^2}x
What is the first derivative of-4e^{-5x^2} ?
The first derivative of-4e^{-5x^2} is 40e^{-5x^2}x