Prove that the set of all differentiable functions :[0,1]→ [0,1] is uncountable.

In my notes, I have something like:

Consider $x \in {[0,1]}$, $f\_{x} (t) = x$ for all $t$ .
$\{h\_{x} | x ∈ [0,1] \}= |[0,1]| = c$ .

I have no idea what this means. Can anyone explain or help me prove it?