Search over 10,000 free study notes

Write key phrases (both basic and sophisticated) on flashcards that you can form answers around as I found that simply memorising answers can lead to freezing and blanking if you forget the whole answer! ...

6cos(2x) +sin(x).Using the double angle formula for cosine (or otherwise), cos(2x) = cos(x)cos(x) - sin(x)sin(x) .cos(2x) = cos^2(x) - sin^2(x) .Hence, 6cos(2x) +sin(x) = 6(cos^2(x) - sin...

The first part of the problem is solved by differentiating once and equating this to zero:
y = x^3 - 3x^2 +4 .dy/dx = 3x^2 - 6x .dy/dx = x(3x - 6...

The answer can be found by using the chain rule and simple substitution as well as basic knowledge of differentiation.f’(x)= -6cos(3x)sin(3x)

You should always start by translating it with 'with,' so for example, 'with the man having laughed,' 'with the man laughing,' or 'with the man being about to laugh.' If you're not sure of the tense, see ...