Introduction: The difference quotient is the slope of the line through $(x,y(x))$ and $(x+\Delta x, y(x+\Delta x))$. Similarly, we have the following theorem.
Theorem: De derivative $y'(x)$ of the function $y(x)$ is equal to the slope of the tangent line at $(x,y(x))$.
Theorem: De derivative $y'(x)$ of the function $y(x)$ is equal to the slope of the tangent line at $(x,y(x))$.