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u² = 2 + xx = u² - 2dx/du = 2u
ʃ x(2 + x))^1/2 dx= ʃ xu dx= ʃ u(u² - 2) dx= ʃ 2u² (u² - 2) du= ʃ 2u⁴ - 4u² du= [...

I would firstly ask them how much they knew about trigonometry, and then guide them through the SoHCaHToA theory. I would use diagrams for this. I would then ask them to spot any ways they could work out ...

The differential of a function is is rate of range of that function. Therefore to find dV/dt, we are finding the rate of change of the volume per unit time.Recall, in order to differentiate a term, e.g. x...

Ok, so the reason we need the Pythagoras theorem is to work out the length of missing side given we know the other 2 sides in a right-angled triangle. (Would go on to draw the triangle with the known side...

This is an example of a question where we would have to use the product rule for differentiation, because we have two functions multiplied together ( x and ln(2x) ).If we have: y = uv, where u and v are f...