DifferentiationPractise the technique of differentiating polynomials and other functions with this self marking exercise. 
This is level 10: interpreting derivatives and second derivatives, maxima, minima and points of inflection. You can earn a trophy if you get at least 7 questions correct and you do this activity online.
You may use a scientific calculator but not a GDC for this exercise
InstructionsTry your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. 




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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy: "3 NQTs in the department, I'm new subject leader in this new academy  Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!" Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." 
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AnswersThere are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer. A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves. Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members. If you would like to enjoy adfree access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe 

Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.  
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© Transum Mathematics :: This activity can be found online at:
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Before beginning these exercises make sure you understand Indices really well.
Level 1  Differentiate basic polynomials
Level 2  Differentiate polynomials including negative and fractional indices
Level 3  Calculations involving the gradient at the given point
Level 4  Finding tangents and normals
Level 5  Differentiate trigonometric functions
Level 6  Differentiate exponential and natural logarithm functions
Level 7  Differentiate using the chain rule
Level 8  Differentiate using the product rule
Level 9  Differentiate using the quotient rule
Level 10  Interpreting derivatives and second derivatives, maxima, minima and points of inflection.
Level 11  Differentiate simple functions parametrically
Exam Style questions are in the style of IB or Alevel exam paper questions and worked solutions are available for Transum subscribers.
Integration  Exercises on indefinite and definite integration of basic algebraic and trigonometric functions.
Please note that if \(y = f(x) = x^2\) then the first differential can be shown in any of the following ways:
$$\frac{dy}{dx} = 2x$$ $$y' = 2x$$ $$f'(x) = 2x$$
In the following rules, \(u\) and \(v\) are functions of \(x\).
if \(x\) and \(y\) are given in terms of a third variable, the parameter, which could be \(t\), then:
$$\frac{dy}{dx} = \frac{dy}{dt} \div \frac{dx}{dt}$$There are many ways you could correctly type in the answers that have a number of terms. The software in this page should recognise most of the commonlyused formats but if you are convinced you have the correct answer but it is being shown as incorrect try typing the answer in a different format. As always, check with your teacher if you are unsure.
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can doubleclick the 'Check' button to make it float at the bottom of your screen.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
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