derivative y=x^3-14x^2+32x+4

解答

导数

y = x^{3} - 14 x^{2} + 32 x + 4

3 x^{2} - 28 x + 32

求解步骤

\frac{d}{d x} (x^{3} - 14 x^{2} + 32 x + 4)

使用微分加减法定则:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (14 x^{2}) + \frac{d}{d x} (32 x) + \frac{d}{d x} (4)

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

\frac{d}{d x} (14 x^{2}) = 28 x

\frac{d}{d x} (32 x) = 32

\frac{d}{d x} (4) = 0

= 3 x^{2} - 28 x + 32 + 0

化简

= 3 x^{2} - 28 x + 32

s \to 0 lim (\frac{- 2 s}{s - 3})

a re a y = - x^{2} + 4, y = 1 - x

\int_{1}^{6} \frac{x ^{2} - 1}{x} d x

y^{^{''}} - 2 y^{^{'}} + 2 y = 2 x - 2, y (0) = 0, y (π) = π

\int 3 x^{3} cos (x^{2}) d x