The image displays an interior view of a classroom or lecture hall, consistent with an educational institution in Vila Real, Portugal

The image displays an interior view of a classroom or lecture hall, consistent with an educational institution in Vila Real, Portugal. A large, white dry-erase board, filled with handwritten mathematical equations and diagrams in black and red marker, dominates the background. Reflections of rectangular windows are visible across the whiteboard's surface. **Whiteboard Content:** - **Left panel:** Contains partial derivative chain rule applications, including a tree diagram illustrating `w=f(s,t)` where `s` and `t` depend on `x` and `y`, followed by expanded derivative formulas. - **Central panel:** Details concepts of directional derivatives, including their limit definition, partial derivatives with respect to standard basis vectors (`e₁`, `e₂`), a two-dimensional Cartesian coordinate system with vectors, the gradient formula (`Dv f(P₀) = ∇f(P₀) ⋅ v`), and the definition of a piecewise function `f(x,y) = (x²y) / (x² + y²) ` for `(x,y) ≠ (0,0)` and `0` for `(x,y) = (0,0)`. - **Right panel:** Partially visible, showing fragments of `∇f(0,0)` and `∂f/∂x`. **Foreground Elements:** - A light-colored desk surface occupies the lower half of the frame. - The top of a dark blue chair back is visible in the lower left. - On the desk, a light brown/beige zippered pencil case is positioned to the left. - To the right, two light purple/mauve pens and one pen with a blue cap rest on a light-colored sheet of paper. - A white "PCSTAR" branded power strip or USB hub with four USB ports is mounted on the textured, light-colored wall, with black cables extending downwards from it. No individuals are present. The scene depicts a static, unoccupied classroom setting.