derivative 2/3 x^3+x^2-12x+12

解答

导数

\frac{2}{3} x^{3} + x^{2} - 12 x + 12

2 x^{2} + 2 x - 12

求解步骤

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

化简

\frac{2}{3} x^{3} + x^{2} - 12 x + 12 : \frac{2 x ^{3}}{3} + x^{2} - 12 x + 12

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

使用微分加减法定则:

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

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

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

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

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

\frac{d}{d x} (12) = 0

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

化简

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

l a pl a ce t r an s f or m f (t) = t

y^{^{'}} = e^{5 x + 4 y}

n = 0 \sum \infty \frac{1}{5}

d er i v a t i v e y = 3 x^{2} + 3 x - 5

\int \frac{1}{4 ( x ^{2} + 1 )} d x