The derivative as the limit of the difference quotient

How does one calculate the slope of the tangent? Starting from the slope of the secant — the difference quotient — and passing to the limit. This section formalises the derivative as a limit, introduces Leibniz notation $\frac{df}{dx}$ and the differential $df = f'(x)\,dx$.

• Difference quotient and derivative
• Leibniz notation
• The differential