Search over 10,000 free study notes

The first part is relatively simple.  If we write tan(3x) as tan(2x+x) we can use addition formulae to give:

tan(2x+x)= (tan(2x)+tan(x))/(1-tan(2x)tan(x))

tan(2x) = 2tan(x)/...

This is a basic example of a very important result: the chain rule. The difficulty of this sort of example is that we have a "function of a function". That is, we have the function '4-x' and ...

For this question the chain rule should be used, the chain rule is that dy/du*du/dx=dy/dx.

If we say u=(x²+2x) and therefore y=e^u

Then du/dx=2x+2 and d...

We can differentiate this implicitly by writing the question as:y = 2^x Then we take the log of both sides:ln(y) = ln(2^x)Using the rules of logartithms this can be written as:ln(y) = ...