derivative f(x)=(x^2-10x)*(x-14)

解

導関数

f (x) = (x^{2} - 10 x) \cdot (x - 14)

3 x^{2} - 48 x + 140

解答ステップ

\frac{d}{d x} ((x^{2} - 10 x) (x - 14))

積の法則を適用:

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

f = x^{2} - 10 x, g = x - 14

= \frac{d}{d x} (x^{2} - 10 x) (x - 14) + \frac{d}{d x} (x - 14) (x^{2} - 10 x)

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

\frac{d}{d x} (x - 14) = 1

= (2 x - 10) (x - 14) + 1 \cdot (x^{2} - 10 x)

簡素化

(2 x - 10) (x - 14) + 1 \cdot (x^{2} - 10 x) : 3 x^{2} - 48 x + 140

= 3 x^{2} - 48 x + 140