展开 1/2 (-(ln(x))/(5x^5)-1/(25x^5))

解答

展开

\frac{1}{2} (- \frac{ln ( x )}{5 x ^{5}} - \frac{1}{25 x ^{5}})

- \frac{ln ( x )}{10 x ^{5}} - \frac{1}{50 x ^{5}}

求解步骤

\frac{1}{2} (- \frac{ln ( x )}{5 x ^{5}} - \frac{1}{25 x ^{5}})

使用分配律:

a (b - c) = ab - a c

a = \frac{1}{2}, b = - \frac{ln ( x )}{5 x ^{5}}, c = \frac{1}{25 x ^{5}}

= \frac{1}{2} (- \frac{ln ( x )}{5 x ^{5}}) - \frac{1}{2} \cdot \frac{1}{25 x ^{5}}

使用加减运算法则

+ (- a) = - a

= - \frac{1}{2} \cdot \frac{ln ( x )}{5 x ^{5}} - \frac{1}{2} \cdot \frac{1}{25 x ^{5}}

化简

- \frac{1}{2} \cdot \frac{ln ( x )}{5 x ^{5}} - \frac{1}{2} \cdot \frac{1}{25 x ^{5}} : - \frac{ln ( x )}{10 x ^{5}} - \frac{1}{50 x ^{5}}

= - \frac{ln ( x )}{10 x ^{5}} - \frac{1}{50 x ^{5}}

e x p an d 3 x + 5 x + 14 x

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s im pl i f y m (m - n)