How do you find the 108th derivative of #y=cos(x)# ?
1 Answer
Aug 21, 2014
The answer is
#d/(dx)cos x=-sin x#
#d/(dx)-sin x=-cos x#
#d/(dx)-cos x=sin x#
#d/(dx)sin x=cos x#
Rather than doing 108 derivatives, we need to calculate 108 modulus 4; this equals 0. Although remainder works for positive dividends, it's best to get used to modulus because this works for negative dividends. Modulus 4 will return either 0, 1, 2, or 3.
#d/(dx)cos x=-sin x# (mod 4=1)
#d/(dx)-sin x=-cos x# (mod 4=2)
#d/(dx)-cos x=sin x# (mod 4=3)
#d/(dx)sin x=cos x# (mod 4=0)
So, our answer is
