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

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

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

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

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derivative of

5 e^{- x^{2}}

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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\frac{d y}{d x} = x + 2 y

\int e^{6} θ sin (7 θ) d θ

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