derivative of (x^2+18(2x+15))

解

\frac{d}{d x} ((x^{2} + 18) (2 x + 15))

6 x^{2} + 30 x + 36

解答ステップ

\frac{d}{d x} ((x^{2} + 18) (2 x + 15))

積の法則を適用:

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

f = x^{2} + 18, g = 2 x + 15

= \frac{d}{d x} (x^{2} + 18) (2 x + 15) + \frac{d}{d x} (2 x + 15) (x^{2} + 18)

\frac{d}{d x} (x^{2} + 18) = 2 x

\frac{d}{d x} (2 x + 15) = 2

= 2 x (2 x + 15) + 2 (x^{2} + 18)

簡素化

2 x (2 x + 15) + 2 (x^{2} + 18) : 6 x^{2} + 30 x + 36

= 6 x^{2} + 30 x + 36