derivative of (3x^2+3(2x^2+1))

解

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

24 x^{3} + 18 x

解答ステップ

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= 6 x (2 x^{2} + 1) + 4 x (3 x^{2} + 3)

簡素化

6 x (2 x^{2} + 1) + 4 x (3 x^{2} + 3) : 24 x^{3} + 18 x

= 24 x^{3} + 18 x