Black-Scholes-Merton Differential Equation

Assume the stock price follows geometric Brownian motion under the physical measure:

$dS=\mu Sdt+\sigma SdW.$

Let $f(S,t)$ be the price of any derivative whose payoff depends only on $S$ and $t$. Derive the Black-Scholes-Merton PDE

$\frac{\partial f}{\partial t}+rS\frac{\partial f}{\partial S}+\frac{1}{2}{\sigma }^2{S}^2\frac{{\partial }^{2}f}{\partial S^2}=rf$

using a delta-hedging / no-arbitrage argument.