derivative y=3(x^2-x+1)(5x-3)

解

導関数

y = 3 (x^{2} - x + 1) (5 x - 3)

3 (15 x^{2} - 16 x + 8)

解答ステップ

\frac{d}{d x} (3 (x^{2} - x + 1) (5 x - 3))

定数を除去:

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

= 3 \frac{d}{d x} ((x^{2} - x + 1) (5 x - 3))

積の法則を適用:

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

f = x^{2} - x + 1, g = 5 x - 3

= 3 (\frac{d}{d x} (x^{2} - x + 1) (5 x - 3) + \frac{d}{d x} (5 x - 3) (x^{2} - x + 1))

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

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

= 3 ((2 x - 1) (5 x - 3) + 5 (x^{2} - x + 1))

拡張

(2 x - 1) (5 x - 3) + 5 (x^{2} - x + 1) : 15 x^{2} - 16 x + 8

= 3 (15 x^{2} - 16 x + 8)