Mark M. answered • 06/07/21
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Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.
f(x) = sinx
f'(x) = cosx
f"(x) = -sinx
f'''(x) = -cosx
f(iv)(x) = sinx etc
Every 4th derivative is the same
So, since 115 = 28R3, the 115th derivative is the same as the 3rd derivative, which is -cosx.
Mark M.
tutor
If you divide 115 by 4 you get 28 with remainder 3. So, if you take the derivative 115 times, you'll cycle through the pattern 28 times and then go 3/4 of the way through the 29th cycle to end up at f'''(x) which is -cosx.
(In my original answer I meant to write: 115/4 = 28R3).
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08/31/22
Andrew S.
I know this answer is correct, but I still do not understand why it is -cos x, and where you got 115=28R3.08/31/22