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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{1}{x 196 x ^{2} - 196} d x

\frac{x ^{2}}{5 + 4 x}

e^{x}, e^{- 3 x}, ln (4)

\frac{d x}{d t} = 1 - x^{2}

\frac{d}{d x} (\frac{3 ( x ^{2} + 2 ) ^{3}}{5})

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