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

Question

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

anonymous · Answer

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.

anonymous · Answer

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.