derivative of (6x+5(x^3-2))

解

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

24 x^{3} + 15 x^{2} - 12

解答ステップ

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

積の法則を適用:

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

f = 6 x + 5, g = x^{3} - 2

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

\frac{d}{d x} (6 x + 5) = 6

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

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

簡素化

6 (x^{3} - 2) + 3 x^{2} (6 x + 5) : 24 x^{3} + 15 x^{2} - 12

= 24 x^{3} + 15 x^{2} - 12