展开 (d((2x-8c)(9-x^2)^2)-2)/(dx)

解答

展开

\frac{d ( ( 2 x - 8 c ) ( 9 - x ^{2} ) ^{2} ) - 2}{d x}

162 - 36 x^{2} + 2 x^{4} - \frac{648 c}{x} + 144 c x - 8 c x^{3} - \frac{2}{d x}

求解步骤

\frac{d ( ( 2 x - 8 c ) ( 9 - x ^{2} ) ^{2} ) - 2}{d x}

去除括号:

(a) = a

= \frac{d ( 2 x - 8 c ) ( 9 - x ^{2} ) ^{2} - 2}{d x}

(9 - x^{2})^{2} = 81 - 18 x^{2} + x^{4}

= \frac{d ( 2 x - 8 c ) ( x ^{4} - 18 x ^{2} + 81 ) - 2}{d x}

乘开

d (2 x - 8 c) (81 - 18 x^{2} + x^{4}) - 2 : 162 d x - 36 d x^{3} + 2 d x^{5} - 648 d c + 144 d c x^{2} - 8 d c x^{4} - 2

= \frac{162 d x - 36 d x ^{3} + 2 d x ^{5} - 648 d c + 144 d c x ^{2} - 8 d c x ^{4} - 2}{d x}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{162 d x - 36 d x ^{3} + 2 d x ^{5} - 648 d c + 144 d c x ^{2} - 8 d c x ^{4} - 2}{d x} = \frac{162 d x}{d x} - \frac{36 d x ^{3}}{d x} + \frac{2 d x ^{5}}{d x} - \frac{648 d c}{d x} + \frac{144 d c x ^{2}}{d x} - \frac{8 d c x ^{4}}{d x} - \frac{2}{d x}

= \frac{162 d x}{d x} - \frac{36 d x ^{3}}{d x} + \frac{2 d x ^{5}}{d x} - \frac{648 d c}{d x} + \frac{144 d c x ^{2}}{d x} - \frac{8 d c x ^{4}}{d x} - \frac{2}{d x}

\frac{162 d x}{d x} = 162

\frac{36 d x ^{3}}{d x} = 36 x^{2}

\frac{2 d x ^{5}}{d x} = 2 x^{4}

\frac{648 d c}{d x} = \frac{648 c}{x}

\frac{144 d c x ^{2}}{d x} = 144 c x

\frac{8 d c x ^{4}}{d x} = 8 c x^{3}

= 162 - 36 x^{2} + 2 x^{4} - \frac{648 c}{x} + 144 c x - 8 c x^{3} - \frac{2}{d x}

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