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.

This is as far as I got.  It seems to get more and more complex.  Even reducing doesn't seem to help.  The third one hasn't been reduced.  I didn't understand the proposed solutions either.  Oh, well.

F(x) = v(1 + 4x^2 - 4x^3 - 4x^5 + 4x^6 + x^8)

F1(x) = (8x-12x^2-20x^4+24x^5+8x^7)/2(v(1+4x^2-4x^3-4x^5+4x^6+x^8))
F2(x) = (4-12x-4x^2-52x^3+72x^4-4x^5+136x^6-112x^7+120x^8-196x^9+96x^10-72x^11+76x^12+12x^14)/((v((1+4x^2-4x^3-4x^5+4x^6+x^8)^3))))
F3(x) = ((0-12-8x-156x^2+288x^3-20x^4+816x^5-784x^6+960x^7-1764x^8+960x^9-792x^10+912x^11+168x^14)(v(1+4x^2-4x^3-4x^5+4x^6+x^8)^3)-((3(1+4x^2-4x^3-4x^5+4x^6+x^8)^2)(8x-12x^2-20x^4+24x^5+8x^7)(4-12x-4x^2-52x^3+72x^4-4x^5+136x^6-112x^7+120x^8-196x^9+96x^10-72x^11+76x^12+12x^14)/(2(v((1+4x^2-4x^3-4x^5+4x^6+x^8)^3))))/(1+4x^2-4x^3-4x^5+4x^6+x^8)^3)

Posted by Joshua on 2010-08-10 12:55:32