- #1
makar
- 3
- 0
Homework Statement
how to find nth derivatives cos^12x and a-x/a+x
Finding the nth Derivatives of cos^12x & a-x/a+x
- Thread starter makar
- Start date
-
- Tags
- Derivatives
Click For Summary
Homework Help Overview
The discussion revolves around finding the nth derivatives of the functions cos12x and (a-x)/(a+x). Participants are exploring methods and approaches to tackle these derivative problems.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Some participants suggest writing out the first few derivatives to identify patterns, while others propose using specific mathematical identities or rules, such as the Leibniz rule, to facilitate the process.
Discussion Status
The discussion is active, with participants sharing different methods and encouraging each other to explore the derivatives. Some guidance has been offered regarding potential approaches, but there is no explicit consensus on a single method yet.
Contextual Notes
Participants are working within the constraints of homework rules, which may limit the amount of direct assistance provided. There is an emphasis on deriving understanding through exploration rather than receiving complete solutions.
how to find nth derivatives cos^12x and a-x/a+x
- #2
makar
- 3
- 0
help please..
- #3
LeonhardEu
- 33
- 3
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.
(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
- 25,837
- 258
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)
try it, and show us what you get
start with the first few derivatives of cos12x
(you may spot a pattern)
- #5
lurflurf
Homework Helper
- 2,459
- 159
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
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
- 0
thank u everyone for helping me..
Similar threads
- · Replies 7 ·
- · Replies 10 ·
- · Replies 15 ·
- · Replies 8 ·
- · Replies 3 ·
- · Replies 27 ·