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

解

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

- 24 x^{5} + 80 x^{4} + 80 x^{3} + 6 x - 12

解答ステップ

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (4 x^{4} - 3) = 16 x^{3}

= (- 2 x + 4) (4 x^{4} - 3) + 16 x^{3} (- x^{2} + 4 x + 5)

簡素化

(- 2 x + 4) (4 x^{4} - 3) + 16 x^{3} (- x^{2} + 4 x + 5) : - 24 x^{5} + 80 x^{4} + 80 x^{3} + 6 x - 12

= - 24 x^{5} + 80 x^{4} + 80 x^{3} + 6 x - 12