derivative of (x+1^3(x-2))

解

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

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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