Study guide and 2 practice problems on:

## First-order approximation of functions of several variables

For a differentiable function $f(x,y)$ and small values of $\Delta x$ and $\Delta y$, we have the first-order approximation
$$f(x+\Delta x,y + \Delta y) \approx f(x, y) + \partial_x f(x, y) \Delta x + \partial_y f(x, y) \Delta y$$