Differentiation under the integration sign on manifolds.

Question

For an oriented manifold $M$ with rank n, a compactly supported n-form $\omega$ and a family of diffeomorphisms $\psi_t:M \rightarrow M$, ($t\in R$) consider the function $f(t)=\int_M \psi_t^*\omega$. ($\psi_t^*$ being the pullback of $\psi_t$).
Under what conditions is it true that $f'(t)=\int_M \frac{\delta}{\delta t}\psi_t^*\omega$ ?