Basic Derivatives - Negative Fractional Power as Radical to Derivative

This math topic focuses on finding the derivatives of functions that are expressed with negative fractional powers and radicals using the power rule. It builds foundational skills in calculus, specifically in manipulation and differentiation of powers that might appear in forms less straightforward than simple polynomials, such as fractional or negative exponents. Each question presents a function involving roots of variables raised to a power, and requires determining the derivative using algebraic conversion of roots to exponents followed by the application of the power rule.