derivative of (x+1*(x^2-1))

解

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

3 x^{2} + 2 x - 1

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

1 \cdot (x^{2} - 1) + 2 x (x + 1) : 3 x^{2} + 2 x - 1

= 3 x^{2} + 2 x - 1