# Differentiation

chain rule, product rule, quotient rule

Teacher recommended

- 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.

## Comments