derivative of (3x^2+4(2x-3))

解

\frac{d}{d x} ((3 x^{2} + 4) (2 x - 3))

18 x^{2} - 18 x + 8

解答ステップ

\frac{d}{d x} ((3 x^{2} + 4) (2 x - 3))

積の法則を適用:

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

f = 3 x^{2} + 4, g = 2 x - 3

= \frac{d}{d x} (3 x^{2} + 4) (2 x - 3) + \frac{d}{d x} (2 x - 3) (3 x^{2} + 4)

\frac{d}{d x} (3 x^{2} + 4) = 6 x

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

= 6 x (2 x - 3) + 2 (3 x^{2} + 4)

簡素化

6 x (2 x - 3) + 2 (3 x^{2} + 4) : 18 x^{2} - 18 x + 8

= 18 x^{2} - 18 x + 8