# Differentiation

chain rule, product rule, quotient rule

HideShow resource information
• Created by: Nicola
• Created on: 24-06-10 01:25

First 129 words of the document:

Product rule ­ to be learnt! Chain rule: Quotient rule ­ to be learnt!
The chain rule is used to differentiate composite
If , then . functions (i.e. functions of a function).
If
It is used when there is a product of 2 functions. The chain rule operates by making the substitution, It is used for differentiating quotients (i.e. fractions).
. Then
Example: Differentiate Example: Differentiate
This is a product of 2 functions: .
Example: Differentiate
Substitute
Using the product rule formula: Differentiate:
So using the chain rule: So,
Factorise top in order to simplify:
So,
Remember these results: Finding the derivative when x = f(y):
We use the result: .
Example: If , find in terms of y.

## Other pages in this set

### Page 2

Here's a taster:

Connected rates of change: Example:
The word rate is associated with differentiation. The volume of a sphere is decreasing at a rate of
Key steps: We want .
20cm3/s. Find the rate at which the radius is
(1) Interpret mathematically the information given in the increasing when the radius is 3 cm.
question.
(2) Write down the relevant formula connecting the Using chain rule:
variables and differentiate it. Solution: From question:
(3) Decide on what quantity needs to be calculated.…read more

## Comments

A really good presentation of Core 3 revision notes.

## Similar Mathematics resources:

See all Mathematics resources »See all resources »