Partial derivatives

Learning objectives

Interpret and use partial derivatives as multipliers with units
Make numerical approximations of partial derivatives using formulas, tables of values, and contour plots
Compute partial derivatives algebraically and with Mathematica
Use the master equation $\Delta z \approx (\partial z/\partial x) \Delta z + (\partial z/\partial y)\Delta y$ for $z=f(x, y)$ and small $\Delta x$ and $\Delta y$
Use a partial derivative in applied contexts
Work with the differential of a multivariable function to produce linear approximations and equations of tangent planes
Use the chain rule to compute partial derivatives of compositions of functions (via variable dependency diagrams )
Compute and interpret second order partial derivatives