Question: Function valued functions

Why does the following derivative vanish?

f:=k->(y->y^k);

h:=z->f(2)(z);

D(h);

 

Note: I am aware that setting h:=f(2) would give the correct result. However, I would like to use the arrow -> notation in a more complicated problem. Also, it seems odd that the plot(h) displays the graph of z->z^2, while D(h) gives 0.

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