# Leibnitz rule

• Apr 23rd 2009, 09:18 AM
dimeola
Leibnitz rule
Hi all,

I'm preparing for my exam and I have no idea how to do this kind of question. :(

part a) Let y= (1-x^2)^1/2 .arccosx. Show that (1-x^2)y' +xy +1-x^2 = 0

part b) Apply the Leibnitz rule to differentiate the equation in part a) n times with respect to x to obtain y(n+1) in terms of y(n-1)

part c) Use the result in Part b to evaluate the Maclaurin series of y up to x^4 .

I can do Part a) only but dunno how to do part b and c...(Headbang)
• Apr 24th 2009, 12:36 AM
CaptainBlack
Quote:

Originally Posted by dimeola
Hi all,

I'm preparing for my exam and I have no idea how to do this kind of question. :(

part a) Let y= (1-x^2)^1/2 .arccosx. Show that (1-x^2)y' +xy +1-x^2 = 0

part b) Apply the Leibnitz rule to differentiate the equation in part a) n times with respect to x to obtain y(n+1) in terms of y(n-1)

part c) Use the result in Part b to evaluate the Maclaurin series of y up to x^4 .

I can do Part a) only but dunno how to do part b and c...(Headbang)

Leibnitz rule

CB