Topic 2 - Differentiation
We have below bronze, silver, gold and platinum tutorials for our Advanced Higher Maths Differentiation topic. Typically as you work through the modules, the difficulty of the skills increase by one step ensuring smooth progression. Simply click on the video to play it and pause it at the relevant points for you to attempt your practice question. Each tutorial has a corresponding worksheet for you to download for additional practice. Make sure you have a pen and paper handy! Be sure to mark your work for every exercise attempted. Good luck!
Essential prior knowledge:-
Higher Maths
- 6.1 - Learning to differentiate at bronze, silver and gold level.
- 13.1 - Further differentiation at bronze, silver and gold level.
Contents:-
2.0 - Introduction to further trigonometric functions
2.1 - The Chain Rule
2.2 - The Product Rule
2.3 - The Quotient Rule
2.4 - The derivatives of inverse trigonometric functions
2.5 - Implicit differentiation
2.6 - Parametric differentiation
2.7 - Logartihmic differentiation
2.8 - Related rates of Change
2.0: Further Trigonometric Functions
Outcome 1
Video 8: Further trigonometric functions. In this video we consolidate trigonometric functions from our prior learning and learn about three new ones.
Now you've watched the video, try these practice questions.
2.1: The Chain Rule
Outcome 1 - Bronze Level
Video 9: The Chain Rule for two functions. In this video we learn how to use the chain rule to differentiate with a function within a function.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [272.8 KB]
Outcome 2 - Silver Level
Video 10: The Chain Rule for more than two functions. In this video we learn how to use the chain rule to differentiate with a function within a function within a function.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [110.3 KB]
Outcome 3 - Gold Level
Video 10: The Chain Rule with Advanced Higher derivatives. In this video we learn about some standard derivatives used in the course and how to use the chain rule to differentiate functions containing them.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [286.1 KB]
SQA Exam Questions
You will find below a collection of Chain Rule SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
2.2: The Product Rule
Outcome 1 - Bronze Level
Video 12: The Product Rule for basic functions. In this video we learn how to create partial fractions for a proper fraction with a denominator consisting of distinct, linear factors.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [103.0 KB]
Outcome 2 - Silver Level
Video 13: The Product Rule with "Bronze/Silver" Chain Rule. In this video we learn how to create partial fractions for a proper fraction with a denominator consisting of distinct, linear factors.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [105.6 KB]
Outcome 3 - Gold Level
Video 14: The Product Rule with "Gold" Chain Rule. In this video we learn how to create partial fractions for a proper fraction with a denominator consisting of distinct, linear factors.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [108.4 KB]
Outcome 4 - Platinum Level
Video 15: The Product Rule with "Advanced Higher" derivatives. In this video we learn how to create partial fractions for a proper fraction with a denominator consisting of distinct, linear factors.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [125.5 KB]
SQA Exam Questions
You will find below a collection of Product Rule SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
2.2 - The Product Rule
- 2019 Question 1(a)
- 2015 Question 2(b)
- 2013 Question 2
- 2012 Question 1(b)
- 2011 Question 3(b)
- 2010 Question 1(a)
- 2009 Question 1(a)
Alternatively you can click here to view all the questions on a playlist.
2.3: The Quotient Rule
Outcome 1 - Bronze Level
Video 16: The Quotient Rule with simple functions. In this video we learn how to use the quotient rule to differentiate a rational function where the numerator and denominator are straight forward to differentiate.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [108.9 KB]
Outcome 2 - Silver Level
Video 17: The Quotient Rule with the Chain Rule. In this video we learn how to use the quotient rule to differentiate a rational function where you will need to use your Chain Rule skills to differentiate the numerator and denominator.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [117.8 KB]
Outcome 3 - Gold Level
Video 18: The Quotient Rule with "Advanced Higher" derivatives. In this video we learn how to use the quotient rule to differentiate a rational function where you will need to use your knowledge of Advanced Higher derivatives to carry out the differentiation.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [119.9 KB]
Outcome 4 - Platinum Level
Video 19: The Quotient Rule with further trigonometric functions. In this video we learn how to use our knowledge of the quotient rule and further trigonometric functions to prove standard derivatives that we have been introduced to before.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [153.8 KB]
SQA Exam Questions
You will find below a collection of Quotient Rule SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
2.3 - The Quotient Rule
- 2019 Question 1(b)
- 2018 Question 1(b)
- 2017 Question 3
- 2016 Question 1(b)
- 2015 Question 2(a)
- 2014 Question 1(a)
- 2012 Question 1(a)
- 2010 Question 1(b)
- 2008 Question 15(a)
Alternatively you can click here to view all the questions on a playlist.
2.4: The Derivatives of Inverse Trigonometric Functions
Outcome 1 - Bronze Level
Video 20: The derivatives of inverse trigonometric functions - sin-1x. In this video we learn the formula for the derivative of sin-1x and how to use it to differentiate associated functions.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [104.7 KB]
Outcome 2 - Silver Level
Video 21: The derivatives of inverse trigonometric functions - cos-1x. In this video we learn the formula for the derivative of cos-1x and how to use it to differentiate associated functions.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [106.5 KB]
Outcome 3 - Gold Level
Video 22: The derivatives of inverse trigonometric functions - tan-1x. In this video we learn the formula for the derivative of tan-1x and how to use it to differentiate associated functions.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [105.4 KB]
SQA Exam Questions
You will find below a collection of Derivatives of Inverse Trig Functions SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
2.4 - The Derivatives of Inverse Trig Functions
Alternatively you can click here to view all the questions on a playlist.
2.5: Implicit Differentiation
Outcome 1 - Bronze Level
Video 23: Implicit differentiation with one 'y' term. In this video we learn how to differentiate expressions that cannot be written with 'y' explicitly as the subject.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [278.7 KB]
Outcome 2 - Silver Level
Video 24: Implicit differentiation with more than one 'y' term. In this video we develop our implicit differentiation skills by having to deal with more than one 'y' term in an expression.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [282.2 KB]
Outcome 3 - Gold Level
Video 25: Implicit differentiation with the product rule. In this video we see how our knowledge of the product rule can help us differentiate more complex expressions using our newly mastered technique.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [284.2 KB]
SQA Exam Questions
You will find below a collection of Implicit Differentiation SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
2.5 - Implicit Differentiation
- 2019 Question 10
- 2018 Question 1(c)
- 2015 Question 4
- 2014 Question 6
- 2013 Question 11
- 2011 Question 3(a)
- 2009 Question 1(b)
- 2008 Question 5
Alternatively you can click here to view all the questions on a playlist.
2.6: Parametric Differentiation
Outcome 1 - Bronze Level
Video 26: Parametric differentiation - the first derivative. In this video we learn how to calculate the first derivative for two curves defined as parametric equations.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [128.4 KB]
Outcome 2 - Silver Level
Video 27: Parametric differentiation - the second derivative. In this video we learn how to calculate the second derivative. Knowing how to calculate the first derivative from the above video is essential here!
Now you've watched the video, try these practice questions.
Adobe Acrobat document [395.2 KB]
Outcome 3 - Gold Level
Video 28: Calculating instantaneous speed. In this video we learn how to calculate the instantaneous speed of a particle where the position is defined by two parametric equations.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [315.6 KB]
SQA Exam Questions
You will find below a collection of Parametric Differentiation SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
2.6 - Parametric Differentiation
- 2019 Question 5
- 2018 Question 6
- 2017 Question 18
- 2016 Question 1(c)
- 2015 Question 8
- 2014 Question 4
- 2012 Question 13
- 2010 Question 13
- 2008 Question 2(b)
- 2007 Question 13
Alternatively you can click here to view all the questions on a playlist.
2.7: Logarithmic Differentiation
Outcome 1 - Bronze Level
Video 29: Logarithmic Differentiation for y = asomething. In this video we learn how to use logarithmic differentiation for a function with x in the power.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [288.4 KB]
Outcome 2 - Silver Level
Video 30: Logarithmic Differentiation for y = xsomething. In this video we develop our logarithmic differentiation skills so we can differentiate trickier functions with x in the power.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [293.4 KB]
Outcome 3 - Gold Level
Video 31: Logarithmic Differentiation as an alternative to the product or the quotient rule. In this video we learn how to use a more efficient method to differentiate functions with powers and roots.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [295.3 KB]
SQA Exam Questions
You will find below a collection of Logarithmic Differentiation SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
2.7 - Logarithmic Differentiation
Alternatively you can click here to view all the questions on a playlist.
2.8: Related Rates of Change
Outcome 1 - Bronze Level
Video 32: Determining related rates of change. In this video we learn how to determine related rates of change by using our powers of clever manipulation!
Now you've watched the video, try these practice questions.
Outcome 2 - Silver Level
Video 33: Calculating related rates of change. Now that we have learned how to determine related rates of change, this video shows us how to calculate them.
Now you've watched the video, try these practice questions.
Outcome 3 - Gold Level
Video 34: Related rates of change in context. In this video we learn how to solve problems in context using our knowledge of related rates of change. This video is well worth a watch!
Now you've watched the video, try these practice questions.
SQA Exam Questions
You will find below a collection of Related Rates of Change SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
2.8 - Related Rates of Change
Alternatively you can click here to view all the questions on a playlist.
Congratulations!
You have completed this module - well done! Remember to go back and redo any areas of weakness, that's how we improve. If you are happy with all areas, go back to the main menu and pick another topic to practice!
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