derivative g(x)=x^3-7x^2+2x+40

解

導関数

g (x) = x^{3} - 7 x^{2} + 2 x + 40

3 x^{2} - 14 x + 2

解答ステップ

\frac{d}{d x} (x^{3} - 7 x^{2} + 2 x + 40)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (7 x^{2}) + \frac{d}{d x} (2 x) + \frac{d}{d x} (40)

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

\frac{d}{d x} (7 x^{2}) = 14 x

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (40) = 0

= 3 x^{2} - 14 x + 2 + 0

簡素化

= 3 x^{2} - 14 x + 2