derivative f(x)=(x^2-1)(1-e^x)

解

導関数

f (x) = (x^{2} - 1) (1 - e^{x})

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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