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sin^(m)x.cos^(n)x...

`sin^(m)x.cos^(n)x`

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Let ` y =sin^(m)x.cos^(n)x`
`:. (dy)/(dx)=(d)/(dx)[(sinx)^(m).(cosx)^(n)]`
`=(sinx)^(m).(d)/(dx)(cosx)^(n)+(cosx)^(n).(d)/(dx)(sinx)^(m)`
`= (sinx)^(m).n(cosx)^(n-1).(d)/(dx)cosx+(cosx)^(n)m(sinx)^(m-1).(d)/(dx)sinx`
`= -nsin^(m)x.cos^(n-1)x.(sinx)+mcos^(n)x. sin^(m-1)x.cosx`
`= -n.sin^(m)x.sinx.cos^(n)x.(1)/(cosx)+m.sin^(m)x.sin^(m)x.(1)/(sinx) .cos^(n)x.cosx`
` = -n.sin^(m)x.cos^(n)x.tanx+msin^(m)x.cos^(n)x.cotx`
`= sin^(m)x.cos^(n)x[-ntanx + mcotx]`
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