C 4 Chapter 4 Differentiation Dr J Frost

C 4 Chapter 4: Differentiation Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com Last modified: 30 th August 2015

Overview In C 3 you significantly increased your ‘toolbox’ for differentiating more complex expressions. In this chapter we’ll broaden your range of differentiation skills: Connect rates of change (When we have more than two variables, each differentiated in terms of each other)

Recap ? ? ? ? ?

SKILL #1: Parametric Differentiation Click for Broanimation Quickfire Questions 2 1 ? 3 ? ?

Test Your Understanding C 4 June 2012 Q 6 ? ?

Exercise 4 A 1 4 a ? b ? ? c d e 3 a ? b ? ? ? ?

SKILL #2: Implicit Differentiation ? ? ?

C 4 Jan 2008 Q 5 ? ? ?

Final Test of Understanding… ?

Exercise 4 B 1 a ? c ? e ? g ? h ? i ? 3 ? 4 ?

What did we do in C 2 when we had a variable in the power? ? ? What now? ? ?

Quickfire Questions ? ? ? ? A not so quickfire question: ?

Test Your Understanding ? ?

Exercise 4 C 2 1 ? b ? ? c d 3 ? 4 ? ?

SKILL #3: Relating Rates of Change Q Firstly, how would we represent… ? ? ? Then by Chain Rule: First copy top and bottom into the diagonals… …Then fill in the gaps with whatever variable you didn’t use. Click for Bromanimation ?

Test Your Understanding June 2012 Q 2 ? ? ?

Exercise 4 D 1 ? 2 ? 3 ? 4 ?

SKILL #4: Setting Up Differential Equations A differential equation is just an equation which contains a mix of variables and derivatives. These often emerge in economics, physics, etc. sometimes because the rate a variable increases/decreases is dependent on the value of the variable itself. For example: Q ? Note: You will learn how to solve differential equations later in C 4. Q ?