Help with interpretation of Mathematica expressions

Hello,

Let p, a, b > 0 and we define
f[a, b] := p^(a + b)

Typing in Mathematica

D[f[a, b], a]

gives

p^{a + b}Log[p]

as expected.

Now we define

h[t] := f[-t, t]

and enter

D[h[t], t]

which gives

f^{(0, 1)}[-t, t] - f^{(1, 0)}[-t, t].

How do we interpret f^{(0, 1)} and f^{(1, 0)}?
As the partial derivatives of f?
But the function h[t] has only one variable?!
So, I would think that by definition
h[t] = p^{-t + t} = 1 and therefore
D[h[t], t] = 0.

Could someone please explain that to me?

Cheers,

Simon

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