Transum Software

Differentiation

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

L 1 L 2 L 3 L 4 Level 5 L 6 L 7 L 8 L 9 L 10 L 11 Exam-Style Description Help

This is level 5: differentiate trigonometric functions. You can earn a trophy if you get at least 7 questions correct and you do this activity online. Type in the terms of your answer in the same order as they appeared in the question. 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.

$$y=3\sin x$$

\(\frac{dy}{dx}=\) Correct Wrong

$$y=7\cos x$$

\(\frac{dy}{dx}=\) Correct Wrong

$$y=6x-5\cos x$$

\(\frac{dy}{dx}=\) Correct Wrong

$$y=3\sin x - 4x^2$$

\(\frac{dy}{dx}=\) Correct Wrong

$$y=9\tan x - 17$$

\(\frac{dy}{dx}=\) Correct Wrong

$$y=\frac{1}{9} \tan x + 19\cos x$$

\(\frac{dy}{dx}=\) Correct Wrong

$$y=\frac{3}{x}-4\cos x$$

\(\frac{dy}{dx}=\) Correct Wrong

$$y=5\sin x - 10 \sqrt x$$

\(\frac{dy}{dx}=\) Correct Wrong

$$y=3\tan x - 2x^{3.9}$$

\(\frac{dy}{dx}=\) Correct Wrong

Check

This is Differentiation level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6 Level 7 Level 8 Level 9 Level 10 Level 11

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.

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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If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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Description of Levels

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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 - Find 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 A-level exam paper questions and worked solutions are available for Transum subscribers.

Integration - Exercises on indefinite and definite integration of basic algebraic and trigonometric functions.

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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Example

The video above is from MathMateVideos.

Mathematical Notation

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 3x2.

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.

Terminology and symbols

Please note that if \(y = f(x) = x^2\) then the first differential can be shown in any of the following ways:

$$\frac{dy}{dx} = 2x$$ $$y' = 2x$$ $$f'(x) = 2x$$

Differentiating Trigonometric Functions

$$\frac{d}{dx} (\sin x) = \cos x $$ $$\frac{d}{dx} (\cos x) = -\sin x $$ $$\frac{d}{dx} (\tan x) = \frac{1}{\cos^2 x} $$

Differentiating Other Functions

$$\frac{d}{dx} (e^x) = e^x $$ $$\frac{d}{dx} ( \ln x) = \frac{1}{x} $$

 

In the following rules, \(u\) and \(v\) are functions of \(x\).

The Product Rule

$$ \text{If} \quad y = uv \quad \text{then}$$ $$\frac{dy}{dx} = v\frac{du}{dx} + u\frac{dv}{dx}$$

The Quotient Rule

$$ \text{If} \quad y = \frac{u}{v} \quad \text{then}$$ $$\frac{dy}{dx} = \frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}$$

The Chain Rule

$$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$$

Answer format

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 commonly-used 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 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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