Math Help - Leibnitz rule

1. 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...

2. 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...
Leibnitz rule

CB