1.3: 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 \[\label{eq:1}f'(x)=\underset{h\to 0}{\lim}\frac{f(x+h)-f(x)}{h}\]