derivative of (5x^2-9(8x+3))

解

\frac{d}{d x} ((5 x^{2} - 9) (8 x + 3))

120 x^{2} + 30 x - 72

解答ステップ

\frac{d}{d x} ((5 x^{2} - 9) (8 x + 3))

積の法則を適用:

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

f = 5 x^{2} - 9, g = 8 x + 3

= \frac{d}{d x} (5 x^{2} - 9) (8 x + 3) + \frac{d}{d x} (8 x + 3) (5 x^{2} - 9)

\frac{d}{d x} (5 x^{2} - 9) = 10 x

\frac{d}{d x} (8 x + 3) = 8

= 10 x (8 x + 3) + 8 (5 x^{2} - 9)

簡素化

10 x (8 x + 3) + 8 (5 x^{2} - 9) : 120 x^{2} + 30 x - 72

= 120 x^{2} + 30 x - 72