0.3: Definition of the Derivative
The derivative of the function \(y = f(x)\), denoted as \(f' (x)\) or \(dy/dx\), is defined as the slope of the tangent line to the curve \(y = f(x)\) at the point \((x, y)\). This slope is obtained by a limit, and is defined as
\[f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}.\label{eq:1} \]