Implicit differentiation can be used to find the derivative of one variable, say y,  with respect to another, say x, even if we cannot explicitly solve an equation to get y in terms of x. Here is a good tutorial on implicit differentiation with many worked out examples.  The authors of this page use the notation D[f(x)] instead of d/dx (f(x)) as we would use, but the ideas are the same.   The example problems get more and more difficult as the number of the problem increases, but try to work through most of them (be sure to look over the trigonometry related problems, #3 and #6).  There are additional practice problems here and here with nicely worked out solutions (using the same notation and techniques we use in class). 

 Once you've mastered implicit differentiation, you are prepared to consider the application topic of related rates.  Carefully read section 3.9 in our textbook and try some of the homework problems.  Students often find Related Rates problems challenging (they are mostly "word" problems) so you do not want to leave this until the night before the next quiz or exam.  When you have completed the reading of section 3.9, print this worksheet and attempt the problems.