derivative f(x)=(8(x^3-6x^2+12x))

解答

导数

f (x) = (8 (x^{3} - 6 x^{2} + 12 x))

8 (3 x^{2} - 12 x + 12)

求解步骤

\frac{d}{d x} (8 (x^{3} - 6 x^{2} + 12 x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (x^{3} - 6 x^{2} + 12 x)

使用微分加减法定则:

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

= 8 (\frac{d}{d x} (x^{3}) - \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (12 x))

\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

= 8 (3 x^{2} - 12 x + 12)

\frac{\partial}{\partial x} (\frac{cos ( x ^{2} \cdot y )}{z ^{3}})

im pl i c i t \frac{d y}{d x}, 5 x y^{5} + 3 x y = 24

d er i v a t i v e arctan (\frac{x}{6})

\frac{\partial}{\partial x} (π \cdot x x^{2} + y^{2})

\frac{d}{d x} (ln (\frac{1}{6 + x}))