derivative of (8x^2-2x(5x+9))

解

\frac{d}{d x} ((8 x^{2} - 2 x) (5 x + 9))

120 x^{2} + 124 x - 18

解答ステップ

\frac{d}{d x} ((8 x^{2} - 2 x) (5 x + 9))

積の法則を適用:

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

f = 8 x^{2} - 2 x, g = 5 x + 9

= \frac{d}{d x} (8 x^{2} - 2 x) (5 x + 9) + \frac{d}{d x} (5 x + 9) (8 x^{2} - 2 x)

\frac{d}{d x} (8 x^{2} - 2 x) = 16 x - 2

\frac{d}{d x} (5 x + 9) = 5

= (16 x - 2) (5 x + 9) + 5 (8 x^{2} - 2 x)

簡素化

(16 x - 2) (5 x + 9) + 5 (8 x^{2} - 2 x) : 120 x^{2} + 124 x - 18

= 120 x^{2} + 124 x - 18