Differentiation

Practise the technique of differentiating polynomials with this self marking exercise.

Level 1Level 2Level 3Level 4Exam-StyleDescriptionHelp Video

This is level 1: differentiate basic polynomials. You can earn a trophy if you get at least 9 questions correct and you do this activity online.

 $$y=x^{4}$$ $$\frac{dy}{dx}=$$ $$y=x^{3}$$ $$\frac{dy}{dx}=$$ $$y=x^{2}$$ $$\frac{dy}{dx}=$$ $$y=x$$ $$\frac{dy}{dx}=$$ $$y=x^{2}+x$$ $$\frac{dy}{dx}=$$ $$y=x^{3}-x^{2}$$ $$\frac{dy}{dx}=$$ $$y=x^{2}+5$$ $$\frac{dy}{dx}=$$ $$y=6x^{3}$$ $$\frac{dy}{dx}=$$ $$y=8x$$ $$\frac{dy}{dx}=$$ $$y=7x^{4}-9x^{3}-6$$ $$\frac{dy}{dx}=$$ $$y=2x^{4}-2x^{3}-9$$ $$\frac{dy}{dx}=$$ $$y=8x^{4}+5x^{3}+8$$ $$\frac{dy}{dx}=$$
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This is Differentiation level 1. You can also try:
Level 2 Level 3 Level 4

Instructions

Try 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.

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Description of Levels

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Level 1 - Differentiate basic polynomials

Level 2 - Differentiate more polynomials

Level 3 - Find the gradient at the given point

Level 4 - Mixed differentiation questions

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

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.

Example

The video above is from MathMateVideos.

Terminology and symbols

Please note that if $$y = f(x) = x^2$$ then the first differential can be shown as:

$$\frac{dy}{dx} = 2x$$

or...

$$y' = 2x$$

or...

$$f'(x) = 2x$$

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 double-click 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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