Answer:
sin(mod(π/2 -x, π) -π/2) . . . . except undefined at odd multiples of π/2
Step-by-step explanation:
The derivative of the modulus of the cosine function is the same as the derivative of the cosine function between cusps: -sin(x), for -π/2 < x < π/2.
There are many ways to make that pattern repeat with period π. one of them is this:
(d/dx)|cos(x)| = sin(mod(π/2 -x, π) -π/2) . . . . . except undefined at x=π/2+kπ, k any integer
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The graph shows the modulus of the cosine function along with its derivative as computed by the graphing calculator and its derivative as defined above.
