derivative (x^4)/4+7/6 x^3-x^2+6x-8

解答

导数

\frac{x ^{4}}{4} + \frac{7}{6} x^{3} - x^{2} + 6 x - 8

x^{3} + \frac{7 x ^{2}}{2} - 2 x + 6

求解步骤

\frac{d}{d x} (\frac{x ^{4}}{4} + \frac{7}{6} x^{3} - x^{2} + 6 x - 8)

化简

\frac{x ^{4}}{4} + \frac{7}{6} x^{3} - x^{2} + 6 x - 8 : \frac{x ^{4}}{4} + \frac{7 x ^{3}}{6} - x^{2} + 6 x - 8

= \frac{d}{d x} (\frac{x ^{4}}{4} + \frac{7 x ^{3}}{6} - x^{2} + 6 x - 8)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{x ^{4}}{4}) + \frac{d}{d x} (\frac{7 x ^{3}}{6}) - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (6 x) - \frac{d}{d x} (8)

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

\frac{d}{d x} (\frac{7 x ^{3}}{6}) = \frac{7 x ^{2}}{2}

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

\frac{d}{d x} (6 x) = 6

\frac{d}{d x} (8) = 0

= x^{3} + \frac{7 x ^{2}}{2} - 2 x + 6 - 0

化简

= x^{3} + \frac{7 x ^{2}}{2} - 2 x + 6