derivative f(x)=(3x^2-2)(5x+5)

解

導関数

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

45 x^{2} + 30 x - 10

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

6 x (5 x + 5) + 5 (3 x^{2} - 2) : 45 x^{2} + 30 x - 10

= 45 x^{2} + 30 x - 10