Word Count : 258

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The energy dispersion relation is given as: [ \varepsilon(\vec{k}) = 2 t_x \cos(k_x a_x) - 2 t_y \cos(k_y a_y) - 2 t_z \cos(k_z a_z) ] The inverse mass tensor components are defined by: [ \left(\frac{1}{m^*}\right)_{ij} = \frac{1}{\hbar^2} \frac{\partial^2 \varepsilon(\vec{k})}{\partial k_i \partial k_j}, \quad i,j = x,y,z ] --- Step 1: Compute diagonal components 1. For (i = j = x): [ \frac{\partial \varepsilon}{\partial k_x} ______ ___ ___ _________ __________ __________ ______ ______ _____ ___ __________ ____.
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