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# $$VerY$$ $$CompleX$$ $$DerivativE$$

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
2 years, 7 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 · 2 years, 6 months ago

6*e^i((π/2)+6x) · 2 years, 7 months ago

Use De Moivre's formula, $${ e }^{ inx }=cos(nx)+isin(nx)$$ · 2 years, 7 months ago

just tell me the answer i know it's easy. · 2 years, 7 months ago

$${ e }^{ i\cdot [n(n+1)/2]\cdot x }\cdot i\cdot n(n+1)/2$$ · 2 years, 7 months ago

correct answer · 2 years, 7 months ago

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 · 2 years, 7 months ago