F(x) is a function which is defined as:
F(x) = √(1 + 4x² - 4x³ - 4x⁵ + 4x⁶ + x⁸)

Determine F⁽¹⁰⁾(0), that is, the tenth derivative of F(x) with respect to x at x=0.

ans: zero

sol:

f'=1/2*p^(-1/2)*p'    where p=1+4x^2+   ...+x^8

f''=1/2*(-1/2)*p^(-3/2)*p'  + 1/2*p^(-1/2)*p''

etc etc

f'''''''''''-polinom consisting of members like a*p^b*p'''' ,all

 members being  equal to zero since all derivatives are 0 at x=0 

 

  

Posted by Ady TZIDON on 2010-08-04 18:10:48