Asked by Dave
Find the 999th derivative of cos x.
I got sin x.
I got sin x.
Answers
Answered by
Reiny
1st derivative: -sinx
2nd derivative: -cosx
3rd derivative: sinx
4th derivative: cosx
5th derivative: -sinx
..
14th derivative:
etc.
notice we are in a cyclical loop of 4 results,
notice 999 leaves a remainder of 3 when divided by 4, so the result is the same as
the 3rd derivative, namely
sinx
2nd derivative: -cosx
3rd derivative: sinx
4th derivative: cosx
5th derivative: -sinx
..
14th derivative:
etc.
notice we are in a cyclical loop of 4 results,
notice 999 leaves a remainder of 3 when divided by 4, so the result is the same as
the 3rd derivative, namely
sinx
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