Partial derivative of integral

Question

Suppose; \begin{array}{l} de = fdt\\ V = {e^T}(t)\;P\;e(t)\; + \;\int\limits_{t - h}^t {{e^T}(\tau )\;Q\;e} (\tau )\;d\tau \end{array}

Does the following equation hold?!

\begin{array}{l} \frac{{\partial V}}{{\partial t}} + \frac{{\partial V}}{{\partial e}}\;f\;\mathop = \limits^? \;\left( {\frac{{dV}}{{dt}}or\;\dot V} \right) \end{array}

Answer 1

Hint: This image solves the problem.