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

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

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

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

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

(- 5, - 2), (5, 12)

y^{^{''}} + \frac{1}{2} y^{^{'}} + \frac{1}{16} y = 0, y (0) = 0, y^{^{'}} (0) = 5

\frac{\partial}{\partial y} (e^{x y} - z)

y^{^{''}} + 12 y^{^{'}} + 37 y = 0

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