The correct answer is (a) \(\frac{d}{dx}(k\frac{dT}{dx})\)
For explanation I would say: The general one-dimensional steady-state diffusion equation is:
\(\frac{d}{dx}(\frac{\Gamma d\phi}{dx})+S=0 \)
For heat conduction problem, the diffusion constant is the heat conductivity (Γ=k) and the flow variable is temperature (Φ=T). As the given problem is source free, S=0. Therefore, the equation becomes
\(\frac{d}{dx}(k\frac{dT}{dx})=0\).