What is the derivative of-10e^{-x^2}x ?

The derivative of-10e^{-x^2}x is -10(-2e^{-x^2}x^2+e^{-x^2})

What is the first derivative of-10e^{-x^2}x ?

The first derivative of-10e^{-x^2}x is -10(-2e^{-x^2}x^2+e^{-x^2})

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derivative of

- 10 e^{- x^{2}} x

- 10 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}})

Solution steps

\frac{d}{d x} (- 10 e^{- x^{2}} x)

Take the constant out:

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

= - 10 \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

= - 10 (\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

= - 10 ((- 2 e^{- x^{2}} x) x + 1 \cdot e^{- x^{2}})

Simplify

- 10 ((- 2 e^{- x^{2}} x) x + 1 \cdot e^{- x^{2}}) : - 10 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}})

= - 10 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}})

y^{^{'}} = \frac{y + t ^{3}}{t}

\int_{1}^{2} \frac{7}{x ^{3} + 3 x} d x

y^{^{'''}} + 12 y^{^{''}} + 36 y^{^{'}} = 18 x^{2}

x^{3} + 3

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

What is the derivative of-10e^{-x^2}x ?
The derivative of-10e^{-x^2}x is -10(-2e^{-x^2}x^2+e^{-x^2})
What is the first derivative of-10e^{-x^2}x ?
The first derivative of-10e^{-x^2}x is -10(-2e^{-x^2}x^2+e^{-x^2})