What is the derivative of-10e^{-5x^2}x ?

The derivative of-10e^{-5x^2}x is -10(-10e^{-5x^2}x^2+e^{-5x^2})

What is the first derivative of-10e^{-5x^2}x ?

The first derivative of-10e^{-5x^2}x is -10(-10e^{-5x^2}x^2+e^{-5x^2})

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derivative of

- 10 e^{- 5 x^{2}} x

- 10 (- 10 e^{- 5 x^{2}} x^{2} + e^{- 5 x^{2}})

Solution steps

\frac{d}{d x} (- 10 e^{- 5 x^{2}} x)

Take the constant out:

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

= - 10 \frac{d}{d x} (e^{- 5 x^{2}} x)

Apply the Product Rule:

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

f = e^{- 5 x^{2}}, g = x

= - 10 (\frac{d}{d x} (e^{- 5 x^{2}}) x + \frac{d x}{d x} e^{- 5 x^{2}})

\frac{d}{d x} (e^{- 5 x^{2}}) = - 10 e^{- 5 x^{2}} x

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

= - 10 ((- 10 e^{- 5 x^{2}} x) x + 1 \cdot e^{- 5 x^{2}})

Simplify

- 10 ((- 10 e^{- 5 x^{2}} x) x + 1 \cdot e^{- 5 x^{2}}) : - 10 (- 10 e^{- 5 x^{2}} x^{2} + e^{- 5 x^{2}})

= - 10 (- 10 e^{- 5 x^{2}} x^{2} + e^{- 5 x^{2}})

What is the derivative of-10e^{-5x^2}x ?
The derivative of-10e^{-5x^2}x is -10(-10e^{-5x^2}x^2+e^{-5x^2})
What is the first derivative of-10e^{-5x^2}x ?
The first derivative of-10e^{-5x^2}x is -10(-10e^{-5x^2}x^2+e^{-5x^2})