derivative of 6x^4-2x^3-12x^2+3x+3

解答

\frac{d}{d x} (6 x^{4} - 2 x^{3} - 12 x^{2} + 3 x + 3)

24 x^{3} - 6 x^{2} - 24 x + 3

求解步骤

\frac{d}{d x} (6 x^{4} - 2 x^{3} - 12 x^{2} + 3 x + 3)

使用微分加减法定则:

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

= \frac{d}{d x} (6 x^{4}) - \frac{d}{d x} (2 x^{3}) - \frac{d}{d x} (12 x^{2}) + \frac{d}{d x} (3 x) + \frac{d}{d x} (3)

\frac{d}{d x} (6 x^{4}) = 24 x^{3}

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

\frac{d}{d x} (12 x^{2}) = 24 x

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

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

= 24 x^{3} - 6 x^{2} - 24 x + 3 + 0

化简

= 24 x^{3} - 6 x^{2} - 24 x + 3