derivative f(x)= 1/10 x(x-2)(x-3)

解

導関数

f (x) = \frac{1}{10} x (x - 2) (x - 3)

\frac{3 x ^{2} - 10 x + 6}{10}

解答ステップ

\frac{d}{d x} (\frac{1}{10} x (x - 2) (x - 3))

定数を除去:

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

= \frac{1}{10} \frac{d}{d x} (x (x - 2) (x - 3))

積の法則を適用:

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

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

= \frac{1}{10} (\frac{d x}{d x} (x - 2) (x - 3) + \frac{d}{d x} ((x - 2) (x - 3)) x)

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

\frac{d}{d x} ((x - 2) (x - 3)) = 2 x - 5

= \frac{1}{10} (1 \cdot (x - 2) (x - 3) + (2 x - 5) x)

簡素化

\frac{1}{10} (1 \cdot (x - 2) (x - 3) + (2 x - 5) x) : \frac{3 x ^{2} - 10 x + 6}{10}

= \frac{3 x ^{2} - 10 x + 6}{10}