derivative (x(x-1)(x-2)(x-3))/(24)

解

導関数

\frac{x ( x - 1 ) ( x - 2 ) ( x - 3 )}{24}

\frac{2 x ^{3} - 9 x ^{2} + 11 x - 3}{12}

解答ステップ

\frac{d}{d x} (\frac{x ( x - 1 ) ( x - 2 ) ( x - 3 )}{24})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{24} \frac{d}{d x} (x (x - 1) (x - 2) (x - 3))

積の法則を適用:

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

f = x, g = (x - 1) (x - 2) (x - 3)

= \frac{1}{24} (\frac{d x}{d x} (x - 1) (x - 2) (x - 3) + \frac{d}{d x} ((x - 1) (x - 2) (x - 3)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 1) (x - 2) (x - 3)) = 3 x^{2} - 12 x + 11

= \frac{1}{24} (1 \cdot (x - 1) (x - 2) (x - 3) + (3 x^{2} - 12 x + 11) x)

簡素化

\frac{1}{24} (1 \cdot (x - 1) (x - 2) (x - 3) + (3 x^{2} - 12 x + 11) x) : \frac{2 x ^{3} - 9 x ^{2} + 11 x - 3}{12}

= \frac{2 x ^{3} - 9 x ^{2} + 11 x - 3}{12}