derivative of (x-a^3(x-b))

解

\frac{d}{d x} ((x - a)^{3} (x - b))

3 (x - a)^{2} (x - b) + (x - a)^{3}

解答ステップ

\frac{d}{d x} ((x - a)^{3} (x - b))

積の法則を適用:

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

f = (x - a)^{3}, g = x - b

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

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

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

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

簡素化

= 3 (x - a)^{2} (x - b) + (x - a)^{3}