If a function f is differentiable, then is a function f^2 differentiable

I would think this is true, but I am not positive. Does anyone have a counter example showing i is false?

of course it's true -- use the chain rule

d(f^2) = 2 f df

since f is differentiable, df exists.
f exists, and 2 is a scalar, so d(f^2) is differentiable.