I have to find a stochastic differential of $Z(t)=X_1(t)e^{X_2(t)}$, where $dX_1=a_1dt+b_1dW_1$ and $dX_2=a_2dt+b_2dW_2$. I solve it
$dZ(t)=(a_1e^{X_2(t)}+X_1e^{X_2(t)}+\frac{1}{2}X_1(t)e^{X_2(t)}b_2^2)dt+e^{X_2(t)}b_1(t)dW_1(t)+X_1(t)e^{X_2(t)}b_2(t)dW_2(t)$
Is it okay or I have to write it in terms of $Z(t)$ (that is, in the form of a stochastic differential equation). And how to do it with this solution?