For each n, let y^(n) denote the nth derivative of the function y = e^(x) cosx.
Can you suggest a general formula for y^(k), where k is an interger > 0? What is y^(2010)?
The Attempt at a Solution
I got e^(x) (cosx - sinx) for y'
-2e^(x) sinx for y''
-2e^(x) (cosx + sinx) for y''' and
-4e^(x) cosx for y''''
which are right, but I dont see a pattern for the nth derivative, which could help me answer the question.