1. The problem is to derive the equation for actual stress, given by $\sigma_{actual} = \frac{P}{A}$. 2. This formula represents the relationship between the applied force and the area over which it acts. Here, $\sigma_{actual}$ is the actual stress, $P$ is the applied load or force, and $A$ is the cross-sectional area. 3. Stress is defined as force per unit area, which means the force applied divided by the area it acts upon. This is a fundamental concept in mechanics of materials. 4. To derive this, start with the definition of stress: $$\sigma = \frac{\text{Force}}{\text{Area}}$$ 5. Substitute the force with $P$ and the area with $A$, giving: $$\sigma_{actual} = \frac{P}{A}$$ 6. This equation assumes the force is uniformly distributed over the area $A$. If the force is not uniform, this formula gives the average stress. 7. Therefore, the derived formula for actual stress is: $$\boxed{\sigma_{actual} = \frac{P}{A}}$$