derivative f(x)=(x-2)^3+10

解答

导数

f (x) = (x - 2)^{3} + 10

3 x^{2} - 12 x + 12

求解步骤

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

化简

(x - 2)^{3} + 10 : x^{3} - 6 x^{2} + 12 x + 2

= \frac{d}{d x} (x^{3} - 6 x^{2} + 12 x + 2)

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

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

\frac{d}{d x} (6 x^{2}) = 12 x

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

\frac{d}{d x} (2) = 0

= 3 x^{2} - 12 x + 12 + 0

化简

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

\int (3 x^{2} + 2) 2 x^{3} + 4 x + 1 d x

d er i v a t i v e f (x) = ln (x e^{- 3 x})

\int \frac{1}{x ln ( 2 x )} d x

\frac{d ^{2}}{d y d x} (sin (x^{2} y^{2}))

\int x^{2} (x^{3} + 9)^{10} d x