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To find the value of R, use Pythagoras's Theorem using the coeffecients of cos θ and sin θ. The correct answer should be R=5. Expand the expression  R cos(θ – α). Equate the expanded expression with 3 cos...

The product rule is a rule for differentiating products of expressions, i.e. 2 expressions multiplied together. 

The rule is: if y=AB, then dy/dx=AdB/dx +B*dA/dx. This can be rem...

Suppose you have 2 functions: f(x) = 3x², g(x) = log₃(x). These are arbitrary, any functions would work. Evaluate f(g(x)): let y = log₃(x) ( = g(x) ), then f(g(x)) = f(...

The most important thing to remember when differentiating implicitly is that y is a function of x. Rewriting y as y(x) often makes it much clearer. For example, evaluate d/dx (y²): using the...

First, we need to find the value of t when x = 6p°C. We are told that after t minutes the temperature, x, will be 60°C; so we can insert 60 into the equation for x: 

60 = 15 + 70e^(-t/40)...