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Differentiation of Trig functions Part II

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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 ?
Check out other topics in Contents Page
Revise the basics of the differentiation of trig functions

Differentiation and Integration of Trigonometric functions

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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

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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:

Answer

Technique used: Rationalization



i)
Techniques used:
Indices:
Power Law:

From LHS



ii)

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



Using the quadratic formula,



Recall that

therefore

Technique used: Taking log on both sides




Recall that in part (i) we showed that

Interesting question, dont you think ?

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For a revision of surds, click here
For a revision of logarithms, click here
For a revision of indices, click here

Integration Techniques Part II

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"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

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Integrating term by term

Formula:

where c is a constant

Example 1



Example 2



Example 3


Example 4