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### Differentiation of Trig functions Part II Differentiation of trig functions using Chain rule, Product rule and Quotient rule

Example 1
Find

Technique: Use of Chain rule

Example 2
Given that , show that

Technique: use Quotient Rule

What's next ?
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Revise the basics of the differentiation of trig functions

### Differentiation and Integration of Trigonometric functions A lot of students confuse the differentiation of trig functions with the integration of trig functions

The most effective way is to study them together

Remember that:

We can differentiate tan x but we cannot integrate tan x

Example 1
Find

Example 2

Note that

Example 3
Find

Example 4

Note that

### Surds, Log and Indices An interesting question showing these 3 topics can be tested in a single question

Question

Express as

i) Hence show that

ii) Given that , prove that

Techniques tested

Rationalization Indices: Power Law:

Technique used: Rationalization

i)
Techniques used:
Indices:
Power Law:

From LHS

ii)

This part of the question requires us to use the Substitution technique

Recall that

therefore

Technique used: Taking log on both sides

Recall that in part (i) we showed that

Interesting question, dont you think ?

Have an interesting question to share? send me an email at yapye at (@) yahoo dot com dot sg

### Integration Techniques Part II "Anti Chain Rule"

This isnt an official maths term. Just something to help students remember how this technique is applied

Recall the use of chain rule in differentiation

Differentiate with respect to x

Chain rule: "Bring down power, negate power by one multiply by the differentiation of the terms within the brackets"

Integration using "Anti Chain rule":
Increase power by one, divided by new power and the differentiation of the terms within the brackets"

Question 1

Note that there are some limitations to "anti chain rule" You cannot . "Anti chain rule" is ony possible with linear factors

Question 2

Integration as anti differentiation

In question 1,

when we differentiate y, we get

When we integrate , we get back

Question 3

Given that

a) Find

b) Hence evaluate

b)

### Integration techniques Part I Integrating term by term

Formula:

where c is a constant

Example 1

Example 2

Example 3

Example 4