derivative of-2x^3+10-3x^2+12x

解答

\frac{d}{d x} (- 2 x^{3} + 10 - 3 x^{2} + 12 x)

- 6 x^{2} - 6 x + 12

求解步骤

\frac{d}{d x} (- 2 x^{3} + 10 - 3 x^{2} + 12 x)

使用微分加减法定则:

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

= - \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (10) - \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (12 x)

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

\frac{d}{d x} (10) = 0

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (12 x) = 12

= - 6 x^{2} + 0 - 6 x + 12

化简

= - 6 x^{2} - 6 x + 12