Given a stochastic process
$$Z_t = e^{4t} \int_0^{t} e^{-2s} \, \,dB_s$$
where $B$ denotes the standard Brownian Motion.
Determine $dZ_t$.
I tried to make use of Ito's rule, seeing that $Z$ is a function of $t$ and $B$ but I got stuck trying to find the derivative of an integral transform.
I thought maybe applying the product rule of Ito, finding
$$dZ_t = \int_0^{t} e^{-2s} \, \, dB_s \cdot 4e^{4t} \, dt + e^{4t} \cdot e^{-2t} dB$$
But I feel as if this can never be correct...