derivative f(x)=(x^2+5)(8-x)

解

導関数

f (x) = (x^{2} + 5) (8 - x)

16 x - 3 x^{2} - 5

解答ステップ

\frac{d}{d x} ((x^{2} + 5) (8 - x))

積の法則を適用:

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

f = x^{2} + 5, g = 8 - x

= \frac{d}{d x} (x^{2} + 5) (8 - x) + \frac{d}{d x} (8 - x) (x^{2} + 5)

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

\frac{d}{d x} (8 - x) = - 1

= 2 x (8 - x) + (- 1) (x^{2} + 5)

簡素化

2 x (8 - x) + (- 1) (x^{2} + 5) : 16 x - 3 x^{2} - 5

= 16 x - 3 x^{2} - 5