derivative f(x)=(x-1)(x+1)^3

解

導関数

f (x) = (x - 1) (x + 1)^{3}

(x + 1)^{3} + 3 (x + 1)^{2} (x - 1)

解答ステップ

\frac{d}{d x} ((x - 1) (x + 1)^{3})

積の法則を適用:

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

f = x - 1, g = (x + 1)^{3}

= \frac{d}{d x} (x - 1) (x + 1)^{3} + \frac{d}{d x} ((x + 1)^{3}) (x - 1)

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

\frac{d}{d x} ((x + 1)^{3}) = 3 (x + 1)^{2}

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

簡素化

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