Marginal effects

Problem

Consider \(y_i=β_1+β_2x_{i,2}+β_3x_{i,2}^2+β_4x_{i,3}+β_5x_{i,2}x_{i,3}+ε_i\) .

a. Find the marginal effect of \(x_2\)

\[ \frac{∂E\left( y \mid x \right)}{∂x_2}\]

b. Find the marginal effect of \(x_3\)

\[ \frac{∂E\left( y \mid x \right)}{∂x_3}\]