Designed for OCR A Level mathematics.

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