The equation (x)g(N) - m - s(x) = 0 describes the growth rate of phytoplankton at equilibrium, where x is the phytoplankton cell size,

The equation ƒ(x)g(N) - m - s(x) = 0 describes the growth rate of phytoplankton at equilibrium, where x is the phytoplankton cell size, ƒ is the maximum growth rate, N is the nutrient concentration, g represents the nutrient limitation experienced by phytoplankton, m is the mortality rate (a constant), and s is the loss due to sinking. Addressing the question of how phytoplankton evolution affects nutrient concentration requires finding the rate of change of N with respect to x. Using implicit differentiation, show that

xp (N),8(x)f (N)8(x),f - (x),s NP