The correct choice is (a) \(\frac{T(t+\Delta t)-T(t-\Delta t)}{2 \Delta t}\)
To explain: The Crank-Nicolson scheme uses the previous and the next steps to get the derivative at the current step. Expressing it mathematically,
\(\frac{\partial T(t)}{\partial t} = \frac{T(t+\Delta t)-T(t-\Delta t)}{2 \Delta t}\).