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

解答

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

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

求解步骤

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

使用微分加减法定则:

(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)

化简

= 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

t a y l or \frac{1}{x ^{\frac{1}{2}}}

t an g e n t f (x) = 2 x^{2} + x - 1, at x = 1