derivative of x^3+x^2-8x+7

解

\frac{d}{d x} (x^{3} + x^{2} - 8 x + 7)

3 x^{2} + 2 x - 8

解答ステップ

\frac{d}{d x} (x^{3} + x^{2} - 8 x + 7)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (x^{2}) - \frac{d}{d x} (8 x) + \frac{d}{d x} (7)

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

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

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

\frac{d}{d x} (7) = 0

= 3 x^{2} + 2 x - 8 + 0

簡素化

= 3 x^{2} + 2 x - 8