Marginal effects an elasticities in the log-linear model

Problem

\[y=f\left( x_2,x_3 \right)=β_1 \exp{\left( β_2x_2+β_3x_3 \right)}\]

1. Find \(∂y/∂x_2\) and \(∂y/∂x_3\)
2. Find \(\left( ∂y/∂x_2 \right)(1/y)\) and \(\left( ∂y/∂x_3 \right)(1/y)\)
3. Find \(log y\)
4. Find \(∂log y/∂x_2\) and \(∂log y/∂x_3\)