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

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

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

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

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

- 8 e^{- x^{2}} x

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= - 8 e^{- x^{2}} x

(8, 8), (4, 6)

e^{2 x} + 2 e^{2 x} x

\frac{d y}{d t} + a y = b

2 x

\frac{x ^{4} + 36 x ^{2}}{( x ^{2} + 12 ) ^{2}}

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