What is the method used for differentiation?

There are a range of methods commonly used for differentation, but my favoured method is as follows:

E.g. Differentiate 3x^2

1) Separate into three separate parts - the Coefficient (the number at the front, in this case the 3), the letter (can be anything, but x in this question) and the power (in this case ^2, squared). 

2) Firstly, multiply the power by the coefficient, this becomes the coefficient of your answer - here, 3x2=6

3) Now, leave the x as it is, and +1 to the power (so the function is now ^3, cubed)

Thus your answer will be 6x^3. At this point, the question may ask you to find the differential when x is a given value, let's say that is 2. If the question doesn't ask for this, 6x^3 is the answer you should clearly put on your exam paper - make sure the examiner can find and read it easily!

4) To find the gradient (the differential) when x=2, we simply have to substitute 2 into 6x^3. This is 6(2)^3 = 6(8) = 48. Make sure you clearly indicate this is your final answer on the exam paper. 

If you have any more questions, or would like help with other examples/ questions, feel free to ask. The examiners ask these questions in a wide variety of ways, but essentially the working required is exactly the same. You just need to become practised in quickly identifying what they want you to do, so you can adapt quickly! Good luck!

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