The function f(x)=(tan |pi[x-pi]|)/(1+[x...

The function `f(x)=(tan |pi[x-pi]|)/(1+[x]^(2))`, where [x] denotes the greatest integer less than or equal to x, is

A

f(x) is discontinuous at some x

B

f(x) is continuous at all x, but the derivative f'(x) does not exist for some x

C

`f'(x)` exists for all x, but f''(x) does not exist for some x

D

f'(x) exists for all x

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The correct Answer is:

D

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