Right option is (a) \(\frac{\partial S}{\partial x}=\frac{K}{A_e}\)

Explanation: For a linear triangular (i.e., constant-strain triangle) element, the shape function \(\psi_i^e\) and its derivatives are given by \(\psi_i^e=\frac{1}{2A_e}(\alpha_i^e+\beta_i^e x+\gamma_i^e y)\), \(\frac{\partial \psi_i^e}{\partial x}=\frac{\beta_i^e}{2A_e}\) and \(\frac{\partial \psi_i^e}{\partial y}=\frac{\gamma_i^e}{2A_e}\)where Ae is the area of the element, α, β and γ are constants. Note that the derivatives of the shape function are constants.