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# C3 Maths Question

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1. You are given that x=y^2 + 4
i) Find dy/dx in terms of y.
ii) Rearrange x=y^2 + 4 in the form y=g(x)
iii) Differentiate y=g(x) to find dy/dx in terms of x.
iv) Show that dy/dx * dx/dy =1
v) For what values of x are your answers valid.

I have done the first four parts but not sure about last two, help would be appreciated
2. For part 4 just look at your answers to past 1 and 2. If you multiply them together you should get 1.

2y * 1/2y = 2y/2y = 1

Then for part 5 I'm not quite sure which bit they are asking for, but...

when x = y^2 + 4, x ε ℝ (meaning x is any real number)
- this is because you can square any real number (including negatives) and add 4 to any real number (including 0)

when y = (x-4)^1/2, x ≠ 4
- this is because of x was 4 then the bracket would equal 0, and doing 0 to the power of -1/2 results in a math error
3. Thank you very much!

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Updated: June 28, 2016
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