The document discusses finding the equation of the normal line to a curve at a given point using differentiation. It introduces the Quotient Rule for differentiating quotients of functions and notes that the Product Rule is often easier to use. It also attributes the discovery of the Quotient Rule to Gottfried Leibniz in 1677 and provides an example of using it to find stationary points on a curve.

1. Starter Find the equation of the normal in the form ax + by + c = 0 to the curve y = x ln (2x – 1) at the point on the curve where x = 1 .

2. Objective: to differentiate quotients

3. The Quotient Rule The Quotient Rule allows you to differentiate functions such as: However, in many cases, it is easier to use the Product Rule so it should be used selectively. e.g. this quotient could be turned into this product:

4. The Quotient Rule Can you prove the Quotient Rule by writing u = yv and differentiating this product with respect to x? Gottfried Leibniz (1646 – 1716) Leibniz discovered the Quotient Rule in July 1677

5. Example Find and classify the stationary points on the curve:

6. Core 3 & 4 Textbook Exercise 10B Page 170