derivative (9x^2)(-1+2x)

解答

导数

(9 x^{2}) (- 1 + 2 x)

9 (- 2 x + 6 x^{2})

求解步骤

\frac{d}{d x} (9 x^{2} (- 1 + 2 x))

将常数提出:

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

= 9 \frac{d}{d x} (x^{2} (- 1 + 2 x))

使用微分乘法定则:

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

f = x^{2}, g = - 1 + 2 x

= 9 (\frac{d}{d x} (x^{2}) (- 1 + 2 x) + \frac{d}{d x} (- 1 + 2 x) x^{2})

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

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

= 9 (2 x (- 1 + 2 x) + 2 x^{2})

乘开

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

= 9 (- 2 x + 6 x^{2})

\int_{0}^{2 x} sin (2 x) d x

d er i v a t i v e (6 x^{2} + 8)^{6}

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