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

The derivative of-4e^{-2x^2}x is -4(-4e^{-2x^2}x^2+e^{-2x^2})

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

The first derivative of-4e^{-2x^2}x is -4(-4e^{-2x^2}x^2+e^{-2x^2})

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- 2 x^{2}}, g = x

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

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

\frac{d x}{d x} = 1

= - 4 ((- 4 e^{- 2 x^{2}} x) x + 1 \cdot e^{- 2 x^{2}})

Simplify

- 4 ((- 4 e^{- 2 x^{2}} x) x + 1 \cdot e^{- 2 x^{2}}) : - 4 (- 4 e^{- 2 x^{2}} x^{2} + e^{- 2 x^{2}})

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

f (x) = 13 x^{- 3}

x \to 0 lim ((1 + 3 x)^{\frac{5}{x}})

\int 5 x e^{6 x} d x

(e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x} - \frac{5 e ^{\frac{1}{x}}}{x ^{2}})^{^{'}}

t \to 0 lim ((t - 2)^{5})

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