$${\vert \frac{dS}{dx} \vert = \frac{k \vert x \vert}{T} = \frac{(50,0\, \mathrm{N/m})(0,012\, \mathrm{m})}{(273\, \mathrm{K} + 27\, \mathrm{K})} \\ = \underline{\underline{2,0 \times 10^{-3}\, \mathrm{J/K \cdot m}}}}$$