Basic Derivatives - Positive Fractional Power (with Rule) to Derivative

This math topic focuses on finding derivatives using the power rule, specifically for functions with positive fractional powers. The problems emphasize applying the derivative power rule (where if \( f(x) = x^n \), then \( f'(x) = n \cdot x^{n-1} \)) to functions expressed as \( x \) raised to a fractional exponent. The task for each problem is to compute the derivative of a given function by correctly executing the power rule and recognizing the changes in the exponent. This involves basic manipulation of fractional exponents to derive the correct new exponent in the differentiated form.