Question

Find the 90 th derivative of the function ƒ(x)=cos(x)
The answer is function?

Answer 1

every 4th derivative is cos x
90= 2(mod 4)..
so, 90th derivative will be 2nd derivative of cos x, i.e.. -cos x

Answer 2

Thanks!!!

Answer 3

f1(x) = - sin(x)
f2(x) = -cos(x)
f3(x) = sin(x)
f4(x) = cos(x)
..
..
f4n(x) = cos(X)
f4n+1(x) = sin(X)
f4n-2(x) = -cos(X)
f4n-1(x) = -sin(X)

I don't seem to find the general governing rule for all