derivative 3x(2x-1)^3

解答

导数

3 x (2 x - 1)^{3}

3 ((2 x - 1)^{3} + 6 x (2 x - 1)^{2})

求解步骤

\frac{d}{d x} (3 x (2 x - 1)^{3})

将常数提出:

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

= 3 \frac{d}{d x} (x (2 x - 1)^{3})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (2 x - 1)^{3}

= 3 (\frac{d x}{d x} (2 x - 1)^{3} + \frac{d}{d x} ((2 x - 1)^{3}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((2 x - 1)^{3}) = 6 (2 x - 1)^{2}

= 3 (1 \cdot (2 x - 1)^{3} + 6 (2 x - 1)^{2} x)

化简

= 3 ((2 x - 1)^{3} + 6 x (2 x - 1)^{2})

\frac{d}{d x} (1 - sec (x))

\int (x^{1.5} + 9 x^{3.5}) d x

(7 x + 2 y) \frac{d y}{d x} = - 2 x - 7 y

x \to 2 + lim (\frac{x + 4}{x - 2})

x \to 0 lim (\frac{7 x}{∣ x ∣})