derivative of 7/3 x^3-2x^2+10

解答

\frac{d}{d x} (\frac{7}{3} x^{3} - 2 x^{2} + 10)

7 x^{2} - 4 x

求解步骤

\frac{d}{d x} (\frac{7}{3} x^{3} - 2 x^{2} + 10)

化简

\frac{7}{3} x^{3} - 2 x^{2} + 10 : \frac{7 x ^{3}}{3} - 2 x^{2} + 10

= \frac{d}{d x} (\frac{7 x ^{3}}{3} - 2 x^{2} + 10)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{7 x ^{3}}{3}) - \frac{d}{d x} (2 x^{2}) + \frac{d}{d x} (10)

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

\frac{d}{d x} (2 x^{2}) = 4 x

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

= 7 x^{2} - 4 x + 0

化简

= 7 x^{2} - 4 x

\int \frac{12 x + 30}{( x ^{2} + 2 x - 8 )} d x

\frac{\partial}{\partial y} (x^{3} + 3 x^{2} y - y^{4})

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 15, y^{^{'}} (0) = b

x d y - (2 x + 1) e^{- y} d x = 0

\int \frac{1}{( 3 x - 1 )} d x