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Delicate Derivative Derivation II (Posted on 2010-08-03) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

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Some Thoughts Nowhere Near Comment 4 of 4 |

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
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