derivative 2x^3+3x^2-12x+9

解答

导数

2 x^{3} + 3 x^{2} - 12 x + 9

6 x^{2} + 6 x - 12

求解步骤

\frac{d}{d x} (2 x^{3} + 3 x^{2} - 12 x + 9)

使用微分加减法定则:

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

= \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (12 x) + \frac{d}{d x} (9)

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

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

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

\frac{d}{d x} (9) = 0

= 6 x^{2} + 6 x - 12 + 0

化简

= 6 x^{2} + 6 x - 12

x \to 0 + lim ((1 - x)^{\frac{1}{x}})

\frac{d y}{d x} = 3 x^{2} + 1

\int (\frac{sin ( 5 x )}{cos ( 5 x )}) d x

t a y l or ∣ x ∣

\frac{d}{d x} (\frac{1}{6} (e^{3 x} + e^{- 3 x}))