DifferentiationPractise the technique of differentiating polynomials and other functions with this self marking exercise. 
This is level 2: differentiate polynomials including negative and fractional indices. You can earn a trophy if you get at least 9 questions correct and you do this activity online. Type in your answers in descending powers of \(x\) without using brackets. Use index notation for roots where necessary. Use the ^ key to type in a power or index and use the forward slash / to type a fraction. Press the right arrow key to end the power or fraction. Click the Help tab above for more.
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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Before beginning these exercises make sure you understand Indices really well.
You should also have been shown how to differentiate from first principles.
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.
Use the ^ key to type in a power or index then the right arrow or tab key to end the power.
For example: Type 3x^2 to get 3x^{2}.
Use the forward slash / to type a fraction then the right arrow or tab key to end the fraction.
For example: Type 1/2 to get ½.
Fractions should be given in their lowest terms.
A square root sign (if required) should be typed in as \sqrt space then press the right arrow key after typing in the last term in the square root.
These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.
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 \(x\).
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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Richard, Pennsylvania
Sunday, October 9, 2022
"Level 7:
y= sqrt(5x^2 8x)
The answer is (5x4)/sqrt(5x^28x) but for some reason it is marked as wrong. I want to confirm that this isn't an error or anything. Thanks!
[Transum: Thanks for your feedback Richard. You are right. The software stores a number of different versions of the correct answer and the format you chose was missing. I have now corrected this error. Sorry for the inconvenience and thanks again for taking the time to let me know.]"