derivative of (x-4(x+1)(x+5))

解

\frac{d}{d x} ((x - 4) (x + 1) (x + 5))

3 x^{2} + 4 x - 19

解答ステップ

\frac{d}{d x} ((x - 4) (x + 1) (x + 5))

積の法則を適用:

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

f = x - 4, g = (x + 1) (x + 5)

= \frac{d}{d x} (x - 4) (x + 1) (x + 5) + \frac{d}{d x} ((x + 1) (x + 5)) (x - 4)

\frac{d}{d x} (x - 4) = 1

\frac{d}{d x} ((x + 1) (x + 5)) = 2 x + 6

= 1 \cdot (x + 1) (x + 5) + (2 x + 6) (x - 4)

簡素化

1 \cdot (x + 1) (x + 5) + (2 x + 6) (x - 4) : 3 x^{2} + 4 x - 19

= 3 x^{2} + 4 x - 19