Statement
If $f\in C^2$, then
$$ f(B_T)-f(B_0)
\int_0^T f’(B_t),dB_t + \frac12\int_0^T f’’(B_t),dt. $$
Differential form
$$ df(B_t)=f'(B_t)\,dB_t+\frac12 f''(B_t)\,dt. $$Interpretation
Compared with the ordinary chain rule, Brownian motion introduces an extra correction term involving $f''$.