1. The problem asks: What does the first derivative represent in calculus? 2. The first derivative of a function $f(x)$, denoted as $f'(x)$ or $\frac{df}{dx}$, measures the rate at which the function's value changes with respect to changes in $x$. 3. The formula for the first derivative is: $$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$ This represents the slope of the tangent line to the curve at the point $x$. 4. Important rules: - The first derivative gives the instantaneous rate of change, not an average. - It does not represent area under the curve or accumulated sum; those relate to integrals. 5. Therefore, the first derivative represents the slope of the tangent line to the function at a given point. Final answer: d. Slope of the tangent line