derivative (x-9)(x-3)^2

解

導関数

(x - 9) (x - 3)^{2}

3 x^{2} - 30 x + 63

解答ステップ

\frac{d}{d x} ((x - 9) (x - 3)^{2})

積の法則を適用:

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

f = x - 9, g = (x - 3)^{2}

= \frac{d}{d x} (x - 9) (x - 3)^{2} + \frac{d}{d x} ((x - 3)^{2}) (x - 9)

\frac{d}{d x} (x - 9) = 1

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

= 1 \cdot (x - 3)^{2} + 2 (x - 3) (x - 9)

簡素化

1 \cdot (x - 3)^{2} + 2 (x - 3) (x - 9) : 3 x^{2} - 30 x + 63

= 3 x^{2} - 30 x + 63