The derivative of the whole thing is still 0. For
$p(y) = a + b y$
we have
$p'(y) = b$
so the integrand
$1/p(y) * u(p) * p'(y)$
collapses to
$\frac{b u(y)}{a + b y}$.
Thus the entire expression whose derivative you want is:
$p(x) \int_x^h \frac{b u(y)}{a + b y} dy$.
The derivative of that with respect to
$y$ — which is what you asked for — is still 0.
Or did you really
want the derivative with respect to
$x$??