Question

how do i find the derivative of y= |cosx| ?

Answer 1

It is piecewise differentiable. The derivative doesn't exist at x=pi/2 + kpi with k an integer.
For\[x \in(-\pi/2,\pi/2)\]\[dy/dx=-sinx\]Further, the function is pi-periodic.

Answer 2

I'm not sure how to state the solution globally. It's probably possible, but will need to be described in positive and negative parts of the cos function. Maybe let \[w \in(-\pi/2,\pi/2)\]\[x=w+2kpi \rightarrow dy/dx=-sinx\]\[x=w+(2k+1)\pi \rightarrow dy/dx=sinx\]As I said before, the derivative is undefined at pi/2 +kpi for k integer.