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y = e^2x(x²+1)^5/2

The first step is to calculate dy/dx. We can do this by splitting y into two parts and using the chain rule of differentiation:

De Moivre's Theorem states that if z = cos(q)+isin(q), then

zⁿ = (cos(q)+isin(q))ⁿ = cos(nq)+isin(nq)

But then 

z^-n = cos(-nq)...

Recall that for two lines to be skew they must satisfy two conditions:

1) They must not be parallel.

2) They must not intersect.

We shall check each condition ...

At GCSE level, proof questions are relatively rare and largely will all require a similar sort of approach. The difference with A Level is that the syllabus contains more than one method of proof. You wil...

A body in a stationary orbit will always remain above the same point on the planet as it orbits. For a body to be in such an orbit, it must rotate around the planet in the same direction as the spin of...