Deriving Ito process with a drift from geometric Brownian motion.

Question

Please help me solve this question. Thank you.

Let the Geometric Brownian motion be: $$ \frac{\Delta S}{S} = \mu \Delta t + \sigma \epsilon \sqrt{\Delta t} $$

$\Delta S$ = change in stock price (s)

$\mu$ = expected rate of return

$\sigma$ = volatility of shock

$epsilon$ has standard normal N(0,1) distribution

$\sigma \epsilon \sqrt{\Delta t}$ = stochastic companion

i) Derive the Ito process with a drift for the above ii) Given that the option price at time $t$ is $f(s,t)$, derive the process with Ito's lemma. Give an example.