derivative 6x(x^2-1)^2

解答

导数

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

6 (5 x^{4} - 6 x^{2} + 1)

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

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

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

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

\frac{d}{d x} ((x^{2} - 1)^{2}) = 4 x (x^{2} - 1)

= 6 (1 \cdot (x^{2} - 1)^{2} + 4 x (x^{2} - 1) x)

化简

6 (1 \cdot (x^{2} - 1)^{2} + 4 x (x^{2} - 1) x) : 6 (5 x^{4} - 6 x^{2} + 1)

= 6 (5 x^{4} - 6 x^{2} + 1)

\int x^{3} 0. 2^{- x} x d x

x \to + (- 2) lim (\frac{8}{x})

t a y l or 9 x ln (1 + 2 x)

\frac{d}{d x} (ln (x + y^{2}))

x \frac{d y}{d x} = y^{2} - y, y (\frac{1}{4}) = \frac{1}{4}