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find the derivative of \((\cos { x } +i\sin { x) } (\cos { 2x+i\sin { 2x)(\cos { 3x } +i\sin { 3x) } ......(cosnx+i\sin { nx) } } } \)

Note by Rishabh Jain
3 years, 4 months ago

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e^ix(1+2+3+....+n)=e^ixn(n+1)/2 So derivative is in(n+1)/2e^ixn(n+1)/2 Pranjal Shukla · 3 years, 2 months ago

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6*e^i((π/2)+6x) Aditi Agarwal · 3 years, 4 months ago

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Use De Moivre's formula, \({ e }^{ inx }=cos(nx)+isin(nx)\) Akash Shah · 3 years, 4 months ago

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@Akash Shah just tell me the answer i know it's easy. Rishabh Jain · 3 years, 4 months ago

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@Rishabh Jain \({ e }^{ i\cdot [n(n+1)/2]\cdot x }\cdot i\cdot n(n+1)/2\) Akash Shah · 3 years, 4 months ago

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@Akash Shah correct answer Prajwal Kavad · 3 years, 4 months ago

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@Rishabh Jain use de moivre's theorem an then it will come like e power n into n+1 into x into i then use chain rule and differentiate Prajwal Kavad · 3 years, 4 months ago

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such a simple one but i cant type the answer properly Prajwal Kavad · 3 years, 4 months ago

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