An example of a function of a function which often occurs is the so-called power function where is any rational number. This is an example of a function of a function in which
Thus, using the chain rule: if then
For example, if then .
Find the derivatives of the following power functions
is the conventional way of writing
. Now find its derivative:
which we would normally write as
Use the function of a function approach again:
Use the function of a function approach first, and then look for a quicker way in this case:
Note that directly - a much quicker way.
Obtain the derivatives of the following functions:
- (remember )