derivative of (x-1*e^{x^2-4})

解

\frac{d}{d x} ((x - 1) \cdot e^{x^{2} - 4})

e^{x^{2} - 4} + 2 e^{x^{2} - 4} x (x - 1)

解答ステップ

\frac{d}{d x} ((x - 1) e^{x^{2} - 4})

積の法則を適用:

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

f = x - 1, g = e^{x^{2} - 4}

= \frac{d}{d x} (x - 1) e^{x^{2} - 4} + \frac{d}{d x} (e^{x^{2} - 4}) (x - 1)

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

\frac{d}{d x} (e^{x^{2} - 4}) = e^{x^{2} - 4} \cdot 2 x

= 1 \cdot e^{x^{2} - 4} + e^{x^{2} - 4} \cdot 2 x (x - 1)

簡素化

= e^{x^{2} - 4} + 2 e^{x^{2} - 4} x (x - 1)