Search over 10,000 free study notes

The product rule is a rule for differentiating products of expressions, i.e. 2 expressions multiplied together. The rule is: if y=A B, then dy/dx=A dB/dx +B*dA/dx. This can be remembered as "Write down ...

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

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 (y 2 ): using the aforementioned...

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) Secondly, we can rea...

This fraction can’t be integrated easily, but if we split it using partial fractions, these will be easier to integrate. To do this, we need to factoise the denominator, as this will follow the method of par...