# Differentiation

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

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

This is level 4: mixed differentiation questions. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

 1. Find $$x$$ if $$f(x)=x^2$$ and $$f'(x)=5$$. 2. Find $$x$$ if $$f(x)=5x^2$$ and $$f'(x)=8$$. 3. Find $$x$$ if $$f(x)=x^2+4x-10$$ and $$f'(x)=6$$. 4. Find $$x$$ if $$f(x)=5x^2+2x-10$$ and $$f'(x)=4$$. 5. Find the equation of the tangent to the curve $$y=x^2+8$$ where the x-coordinate is 1. Write your answer in the form $$y=mx+c$$. 6. Find the equation of the tangent to the curve $$y=5x^2+7$$ where the x-coordinate is -1. Write your answer in the form $$y=mx+c$$. 7. Find the equation of the tangent to the curve $$y=1-x^2$$ where the x-coordinate is -3. Write your answer in the form $$y=mx+c$$. 8. Find the equation of the normal to the curve $$y=3x^2-5x-1$$ where the x-coordinate is 1. Write your answer in the form $$y=mx+c$$ 9. Find the equation of the normal to the curve $$y=9-x^2$$ where the x-coordinate is 0. 10. Find the equation of the tangent to the curve $$y=x^2$$ which is parallel to the x-axis.
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This is Differentiation level 4. You can also try:
Level 1 Level 2 Level 3

## Instructions

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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.

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## 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...

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

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