Derivative of f(x) = |sin(x)-sin(y)| - |x-y| ?

Hi, I'm trying to resolve an MVT problem : http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/unit-2-applications-of-differentiation/part-c-mean-value-theorem-antiderivatives-and-differential-equations/session-35-using-the-mean-value-theorem/MIT18_01SCF10_ex35prb.pdf

But I can't figure out what is the derivative of |sin(x)-sin(y)| - |x-y|. To be more precise, I've seen on the web that it's cos(c) but I don't get the way to the answer.

Question

Derivative of f(x) = |sin(x)-sin(y)| - |x-y| ?

Hi, I'm trying to resolve an MVT problem : http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/unit-2-applications-of-differentiation/part-c-mean-value-theorem-antiderivatives-and-differential-equations/session-35-using-the-mean-value-theorem/MIT18_01SCF10_ex35prb.pdf

But I can't figure out what is the derivative of |sin(x)-sin(y)| - |x-y|. To be more precise, I've seen on the web that it's cos(c) but I don't get the way to the answer.