Derivatives of Elementary Functions
The derivative measures the instantaneous rate of change of a function. Mastering the derivatives of elementary functions is the foundation of all calculus.
Formal Definition
The derivative of a function $f(x)$ is defined as:
$$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$
We write the derivative as $f'(x)$, $\frac{df}{dx}$, or $\frac{d}{dx}[f(x)]$. It gives the slope of the tangent line to the curve at any point $x$.
🎮 Interactive: Explore a Function and Its Derivative
Drag the red point along the curve to see how the tangent line slope changes. The blue curve is $f(x)$ and the orange curve is $f'(x)$.
Interactive visualization — available in the full lesson