derivative of 7-(1.01^{-x^2})

解答

\frac{d}{d x} (7 - (1.01)^{- x^{2}})

0.01990 \dots \cdot 1.0 1^{- x^{2}} x

求解步骤

\frac{d}{d x} (7 - (1.01)^{- x^{2}})

使用微分加减法定则:

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

= \frac{d}{d x} (7) - \frac{d}{d x} (1.0 1^{- x^{2}})

\frac{d}{d x} (7) = 0

\frac{d}{d x} (1.0 1^{- x^{2}}) = - 0.01990 \dots \cdot 1.0 1^{- x^{2}} x

= 0 - (- 0.01990 \dots \cdot 1.0 1^{- x^{2}} x)

化简

= 0.01990 \dots \cdot 1.0 1^{- x^{2}} x

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