- #1

makar

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## Homework Statement

how to find nth derivatives cos^12x and a-x/a+x

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- Thread starter makar
- Start date

- #1

makar

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how to find nth derivatives cos^12x and a-x/a+x

- #2

makar

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help please..

- #3

LeonhardEu

- 33

- 3

(sinx)' = cosx = sin(x+pi/2)

(sinx)'' = (cosx)' = -sinx= sin(x+pi), (sinx)''' = -cosx = sin(x+3pi/2), (sinx)(4) = sinx = sin(x+2pi).

SO the n-nth derivative of sinx is sin(x + n*pi/2)

Yours are all the same way.

- #4

tiny-tim

Science Advisor

Homework Helper

- 25,838

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try it, and show us what you get

start with the first few derivatives of cos

(you may spot a pattern)

- #5

lurflurf

Homework Helper

- 2,460

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1)use

=cos(x)^12=(792 cos(2 x)+495 cos(4 x)+220 cos(6 x)+66 cos(8 x)+12 cos(10 x)+cos(12 x)+462)/2048

2)use the Leibniz rule

http://en.wikipedia.org/wiki/Leibniz_rule_(generalized_product_rule)

For use (a-x)/(a+x)

(a-x)/(a+x)=(2 a)/(a+x)-1

- #6

makar

- 3

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thank u everyone for helping me..

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