Question

Need help finding dy/dx.

Answer 1

oh

Answer 2

\[ f(x)=(\cos x+i \sin x)(\cos 3 x+i \sin 3 x)...(\cos (2n-1)x+i \sin (2n-1)x)\]

Answer 3

or let it be y

Answer 4

Why is there "\(...\)" ??

Answer 5

\[\Huge y= e^{i x n ^2}\]
im stuck here

Answer 6

Well, since you're finding the derivative: \(\frac{dy}{dx}\) everything else is a constant, correct?

Answer 7

umm it continues like that..its a seqence
(cosx+isinx)(cos3x+isin3x)(cos5x+isin5x..so on till 2n-1

Answer 8

yes

Answer 9

Wait, are you trying to find the complimentary solution for this? Is this single-variable Calculus or Ordinary Differential Equations?

Answer 10

single variable calculus

Answer 11

answer is -n^4 which I'm not getting somehow

Answer 12

Can you show me what you did to get \(\large e^{inx^2}\)

Answer 13

Sure.
\[\large (\cos \theta+i \sin \theta)=e^{i \theta}\]
\[\large e^{ix(1+3+5.....(2n-1))}\]
This is an AP..whose sum say S=>
\[\large S= \frac{n}{2}(2+(n-1)2)=\frac{n}{2}(2n)=n^2\]
\[\Huge y=e^{ixn^2}\]

Answer 14

i guess answer is smt like -n^2 . y which im not getting :(

Answer 15

@Yahoo! @ganeshie8 @dan815

Answer 16

is it \(2+(n-1)^2\) or \(2+(n-1)2\)

Answer 17

latter

Answer 18

What?

Answer 19

what is the formula for sum of n terms of an AP?

Answer 20

i know it ,asking you..you seem confused

Answer 21

i am confused lol

Answer 22

d=common difference b/w 2 terms

Answer 23

oops sorry

Answer 24

I didn't learn it that way. Nor have I seen it using the AP

Answer 25

\[\[\LARGE Sum_{AP}=\frac{n}{2}(2(Term_1)+(n-1)d)\]\]

Answer 26

This looks to me like ODE's, tbh. And i am not sure how to approach this using Calc I.

Answer 27

tag sm1 else then :P

Answer 28

oh sorry its done ! made a minor mistake.

Answer 29

nevermind

Answer 30

This looks like eulers relation, idk if you're familiar with, where \(e^{i\theta}=cos(\theta)+isin(\theta)\)

Answer 31

Sorry i wasn't much help. I wanted to help, but I couldn't think of exactly where I have seen this before. Lol

Answer 32

its okay XD

Answer 33

Someday that will make sense to me, lol.

Answer 34

add \(n\) consecutive odd numbers, get \(n^2\)