derivative of (5x^2-3*(x^2+x+4))

解

\frac{d}{d x} ((5 x^{2} - 3) \cdot (x^{2} + x + 4))

20 x^{3} + 15 x^{2} + 34 x - 3

解答ステップ

\frac{d}{d x} ((5 x^{2} - 3) (x^{2} + x + 4))

積の法則を適用:

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

f = 5 x^{2} - 3, g = x^{2} + x + 4

= \frac{d}{d x} (5 x^{2} - 3) (x^{2} + x + 4) + \frac{d}{d x} (x^{2} + x + 4) (5 x^{2} - 3)

\frac{d}{d x} (5 x^{2} - 3) = 10 x

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

= 10 x (x^{2} + x + 4) + (2 x + 1) (5 x^{2} - 3)

簡素化

10 x (x^{2} + x + 4) + (2 x + 1) (5 x^{2} - 3) : 20 x^{3} + 15 x^{2} + 34 x - 3

= 20 x^{3} + 15 x^{2} + 34 x - 3