Can you explain how (5.22) is arrived from (5.21), especially why is there a plus sign on the right and no differentiation for utility on the compensated demand?

To begin our indirect approach, 5 we will assume (as before) there are only two goods (x and y) and focus on the compensated demand function, xc(px,py,U), and its relationship to the ordinary demand function, x(px,py,I). By definition we know that xc(px,py,U)=x[px,py,E(px,py,U)]. This conclusion was already introduced in connection with Figure 5.7, which showed that the quantity demanded is identical for the compensated and uncompensated demand functions when income is exactly what is needed to attain the required utility level. Equation 5.21 is obtained by inserting that expenditure level into the demand function, x(px,py,I). Now we can proceed by partially differentiating Equation 5.21 with respect to px and recognizing that this variable enters into the ordinary demand function in two places. Hence pxxc=pxx+ExpxE To begin our indirect approach, 5 we will assume (as before) there are only two goods (x and y) and focus on the compensated demand function, xc(px,py,U), and its relationship to the ordinary demand function, x(px,py,I). By definition we know that xc(px,py,U)=x[px,py,E(px,py,U)]. This conclusion was already introduced in connection with Figure 5.7, which showed that the quantity demanded is identical for the compensated and uncompensated demand functions when income is exactly what is needed to attain the required utility level. Equation 5.21 is obtained by inserting that expenditure level into the demand function, x(px,py,I). Now we can proceed by partially differentiating Equation 5.21 with respect to px and recognizing that this variable enters into the ordinary demand function in two places. Hence pxxc=pxx+ExpxE