Question

What is the nth derivative of sin^3x?

Answer 1

Using the chain rule.

sin^3(x) = [sin(x)]^3

d/dx[sin(x)]^3∗d/dx[sin(x)]

d/dx sinx = cosx 
d/dx cosx = -sinx 
d/dx (-sinx) = -cosx 
d/dx (-cosx) = sinx
back to where we started from!!! 
So,
repeat repeat repeat !!