Find (d^110/dx^110)(sin x)

Question

Find (d^110/dx^110)(sin x)

Answer 1

d(sin(x))/dx = cos(x)

d^2(sin(x)/dx^2 = -sin(x)

d^3(sin(x)/dx^3) = -cos(x)

d^4(sin(x)/dx^4) = sin(x)

So derivatives divisible by 4 will result in the same as the original. Since 108 is divisible by 4, it will result in sin(x), two more derivatives after that results in -sin(x)