Differentiate correlation of between depth and bouguer anomaly

Assume we measure bouguer anomaly (g) and depth (H) of the certain horizon through a profile at each point. Based on data we get a correlation between H and g and express it with a polynomial equation like $H(g) = a_1g^n+a_2g^{n-1}+…+a_n $. What the derivative of the equation will give us?