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y=log[sin^(3)x.cos^(4)x.(x^(2)-1)^(5)]...

`y=log[sin^(3)x.cos^(4)x.(x^(2)-1)^(5)]`

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`y=log[sin^(3)x.cos^(4)x.(x^(2)-1)^(5)]`
`=logsin^(3)x+logcos^(4)x+log(x^(2)-1)^(5)`
`=3logsinx+4logcosx+5log(x^(2)-1)`
`therefore (dy)/(dx)=3(d)/(dx)(logsinx)+4(d)/(dx)(logcosx)+5(d)/(dx)[log(x^(2)-1)]`
`=3xx(1)/(sinx).(d)/(dx)(sinx)+4xx(1)/(cosx).(d)/(dx)(cosx)+5xx(1)/(x^(2)-1).(d)/(dx)(x^(2)-1)`
`=3xx(1)/(sinx).cosx+4xx(1)/(cosx).(-sinx)+(5)/(x^(2)-1).(2x)`
`=3cotx-4tanx+(10x)/(x^(2)-1)`
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