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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} ((5 x + 4 y) e^{y})

5 x^{2} - 4 x + 5

x \to \infty lim (x e^{x})

\frac{d y}{d x} = \frac{9 x}{7 y}

\frac{d}{d y} (ln (x y))

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