Given f(x) = sin^–1(cos x),

Checking differentiability and continuity,

LHL at x =0,

RHL at x =0,

And

Hence, f(x) is continuous at x =0.

LHD at x =0,

RHD at x =0,

∵ LHD ≠RHD

∴ f(x) is not differentiable at x =0.

Hence, option B is correct.