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

解

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

3 x^{2} + 2 x - 5

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

2 (x - 1) (x + 3) + 1 \cdot (x - 1)^{2} : 3 x^{2} + 2 x - 5

= 3 x^{2} + 2 x - 5