  In this note, we prove a blow-up result for a semilinear generalized Tricomi
equation with nonlinear term of derivative type, i.e., for the equation
$\mathscr{T}_{\!\!\ell} u = |\partial_t u|^p$, where $ \mathscr{T}_{\!\!\ell} =
\partial_t^2-t^{2\ell}\Delta$. Smooth solutions blow up in finite time for
positive Cauchy data when the exponent $p$ of the nonlinear term is below
$\frac{\mathscr{Q}}{\mathscr{Q}-2}$, where $\mathscr{Q}=(\ell+1)n+1$ is the
quasi-homogeneous dimension of the generalized Tricomi operator
$\mathscr{T}_{\!\!\ell}$. Furthermore, we get also an upper bound estimate for
the lifespan.
