The document contains several mathematical problems focusing on derivatives, function properties, and inequalities. Here's a breakdown of each task:

1. Partial Derivatives Calculation:

   • For $f(s, r) = s - 7r^5 + 8s^6r - 3r + 2$, calculate $\frac{\partial f}{\partial r}$.
   • For $x y^3 - 6z x^2 + 3y - 4x z^2 - 9 = 7 x y$, calculate $\frac{\partial z}{\partial y}$ using implicit differentiation.

2. **Inequality Solution