$dX(t) = a(t)dt +b(t)dW(t)$ and $Y(t)=exp(X(t)$ find $dY(t)$

Question

Having trouble with the following

$$dX(t) = a(t) + b(t)dW(t)$$ $$Y(t) =exp(X(t))$$

find $dY(t)$

Answer 1

What is your trouble then?
If you are to exercise your understanding on Ito formula, everything is direct
. $dY(t)= \exp ( X(t))\left[ dX_t+\frac{1}{2}d \langle X \rangle_t \right]=Y_t \left[ dX_t+ \frac{1}{2}b(t)^2dt \right] $