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

解

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

12 x^{3} + 24 x^{2} - 50 x + 24

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (3 x^{2} - x + 5) = 6 x - 1

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

= (6 x - 1) (x^{2} + 3 x - 9) + (2 x + 3) (3 x^{2} - x + 5)

簡素化

(6 x - 1) (x^{2} + 3 x - 9) + (2 x + 3) (3 x^{2} - x + 5) : 12 x^{3} + 24 x^{2} - 50 x + 24

= 12 x^{3} + 24 x^{2} - 50 x + 24