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Making a substitution for u = 2x^2 Now y = ln(u) dy/dx = du/dx * dy/du du/dx = 4x dy/du = 1/u dy/dx = 4x/u Then substitute 2x^2 back in as u The final answer is 4x/(2x^2) Which can be simplified by divid...

This does depend slightly on the essay that you are writing, however as an overarching structure I would use the following:

Start by stating your argument this can be anything about the theory that...

Relevant equations: 1) frequency = 1/ time period; 2) v(max) = Amplitude*(2pifrequency)

First, we need to calculate the frequency of the baby's oscillation. That is, the number of times, p...

f'(x)=-2(3x+4)^(-3) * 3 = -6(3x+4)^(-3);
f''(x)= 18(3x+4)^(-4) * 3 = 54(3x+4)^(-4);
both found by using the chain rule for differentiation.

Then Maclaurin series up to x^2 is: f(x)=f(0)...

For SAQs (Short Answer Questions) in Paper 1, remember that they are worth 8 marks each. You can easily get at least 6 marks if you do the following. I will use the bullet point "Explain one study re...