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Differentiate e^x \ logsin2x with respec...

Differentiate `e^x \ logsin2x` with respect to `x` .

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We have `y=e^x \ logsin2x`
`(dy)/(dx)=(d)/(dx)[e^(x)log(sin 2x)]`
`e^(x).(d)/(dx){log(sin 2x)}+log(sin 2x).(d)/(dx)(e^(x))`
`=e^(x).{(1)/(sin 2x).cos2x.2}+log(sin 2x).e^(x)`
`=2e^(x) cot 2x+e^(x) log (sin 2x)`
`=e^(x){2 cot 2x+log (sin 2x)}`
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