I am struggeling to make sence of the following derivative. Let $Y_t$ be a standard BM and define
$$D_t = \left(\int_0^t Y_s^\gamma \exp(\alpha s)~ds \right)^{1/\gamma}$$
I claim that $D_t$ does not attain a closed-form solution. Yet the question is, if one can solve the derivative
$$\frac{\partial D_t}{\partial Y_t} =~?$$
I tried approximating the integral by Riemann sums, but then the result would be that the derivative is zero (as the derivative of the sum contains a $\Delta t$-term which goes to zero). Is this the correct result?