find the derivative of (cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)......(cosnx+isinnx)(\cos { x } +i\sin { x) } (\cos { 2x+i\sin { 2x)(\cos { 3x } +i\sin { 3x) } ......(cosnx+i\sin { nx) } } } (cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)......(cosnx+isinnx)
Note by Rishabh Jain 7 years ago
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such a simple one but i cant type the answer properly
Use De Moivre's formula, einx=cos(nx)+isin(nx){ e }^{ inx }=cos(nx)+isin(nx)einx=cos(nx)+isin(nx)
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just tell me the answer i know it's easy.
ei⋅[n(n+1)/2]⋅x⋅i⋅n(n+1)/2{ e }^{ i\cdot [n(n+1)/2]\cdot x }\cdot i\cdot n(n+1)/2ei⋅[n(n+1)/2]⋅x⋅i⋅n(n+1)/2
@Akash Shah – correct answer
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
6*e^i((π/2)+6x)
e^ix(1+2+3+....+n)=e^ixn(n+1)/2 So derivative is in(n+1)/2e^ixn(n+1)/2
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Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
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[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
such a simple one but i cant type the answer properly
Use De Moivre's formula, einx=cos(nx)+isin(nx)
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just tell me the answer i know it's easy.
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ei⋅[n(n+1)/2]⋅x⋅i⋅n(n+1)/2
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correct answer
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
6*e^i((π/2)+6x)
e^ix(1+2+3+....+n)=e^ixn(n+1)/2 So derivative is in(n+1)/2e^ixn(n+1)/2