What is the derivative of 1-e^{-x^2} ?

The derivative of 1-e^{-x^2} is 2e^{-x^2}x

What is the first derivative of 1-e^{-x^2} ?

The first derivative of 1-e^{-x^2} is 2e^{-x^2}x

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\frac{d}{d x} (1 - e^{- x^{2}})

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

Solution steps

\frac{d}{d x} (1 - e^{- x^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) - \frac{d}{d x} (e^{- x^{2}})

\frac{d}{d x} (1) = 0

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

= 0 - (- 2 e^{- x^{2}} x)

Simplify

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

x \to 2 lim (x^{4} + 5^{x} - 2)

x \to - 1 lim (2 x^{3} + 3 x^{2} - 6)

\int_{- 1}^{3} x^{2} - 2 x d x

\frac{1}{x ^{\frac{1}{2}}}

f (x) = 2 x^{2} + x - 1, at x = 1

What is the derivative of 1-e^{-x^2} ?
The derivative of 1-e^{-x^2} is 2e^{-x^2}x
What is the first derivative of 1-e^{-x^2} ?
The first derivative of 1-e^{-x^2} is 2e^{-x^2}x