展开-(x^4sin(lx)(-l^2x^2+5))/(l^2)

解答

展开

- \frac{x ^{4} sin ( l x ) ( - l ^{2} x ^{2} + 5 )}{l ^{2}}

x^{6} sin (l x) - \frac{5 x ^{4} sin ( l x )}{l ^{2}}

求解步骤

- \frac{x ^{4} sin ( l x ) ( - l ^{2} x ^{2} + 5 )}{l ^{2}}

乘开

x^{4} sin (l x) (- l^{2} x^{2} + 5) : - l^{2} x^{6} sin (l x) + 5 x^{4} sin (l x)

= - \frac{- l ^{2} x ^{6} sin ( l x ) + 5 x ^{4} sin ( l x )}{l ^{2}}

使用分式法则:

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

\frac{- l ^{2} x ^{6} sin ( l x ) + 5 x ^{4} sin ( l x )}{l ^{2}} = - (- \frac{l ^{2} x ^{6} sin ( l x )}{l ^{2}}) - (\frac{5 x ^{4} sin ( l x )}{l ^{2}})

= - (- \frac{l ^{2} x ^{6} sin ( l x )}{l ^{2}}) - (\frac{5 x ^{4} sin ( l x )}{l ^{2}})

去除括号:

(a) = a, - (- a) = a

= \frac{l ^{2} x ^{6} sin ( l x )}{l ^{2}} - \frac{5 x ^{4} sin ( l x )}{l ^{2}}

消掉

\frac{l ^{2} x ^{6} sin ( l x )}{l ^{2}} : x^{6} sin (l x)

= x^{6} sin (l x) - \frac{5 x ^{4} sin ( l x )}{l ^{2}}

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