derivative of x^3-5x^2+7x-3

解

\frac{d}{d x} (x^{3} - 5 x^{2} + 7 x - 3)

3 x^{2} - 10 x + 7

解答ステップ

\frac{d}{d x} (x^{3} - 5 x^{2} + 7 x - 3)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (7 x) - \frac{d}{d x} (3)

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

\frac{d}{d x} (5 x^{2}) = 10 x

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

\frac{d}{d x} (3) = 0

= 3 x^{2} - 10 x + 7 - 0

簡素化

= 3 x^{2} - 10 x + 7