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Desperately Difficult Derivative (Posted on 2005-03-30) Difficulty: 4 of 5
If f(x)=sin(x), find the value of its 2001st derivative, at x=0.

See The Solution Submitted by Old Original Oskar!    
Rating: 3.8000 (5 votes)

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solution? | Comment 1 of 9

In a quick approach it seems that the only terms that could take a value different from 0 are those where the third derivate of x^3 (=6) appears alone. 

If I haven't made mistakes, in pair derivatives we have       6*sin (x^3), and in impars we have 6*cos (x^3) (and with sign changing).  For 2001st derivatives the sign would be negative and the value would be -6.

  Posted by armando on 2005-03-30 19:27:14
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