Finding the nth derivative of cos^12(x) and (a-x)/(a+x)

[makar]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[makar]

help please..

 

[LeonhardEu]

Don't panic. Since you know derivation is quite easy to deduce them. Write the first two or three derivatives and see the pattern. I 'll give an example to understand:
(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.

 

[tiny-tim]

hi makar! welcome to pf!

try it, and show us what you get

start with the first few derivatives of cos¹²x

(you may spot a pattern)

 

[lurflurf]

There are two ways to go

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

 

[makar]

thank u everyone for helping me..