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Survey of Calculus – Section 3.6 – Implicit Differentiation and Related Rates Until now all the functions you have seen in this class have been written explicitly. That just means that y has been isolated. Now we will learn how to find the derivative when a function is written implicitly. In other words, how do we find the derivative if it is difficult or impossible to isolate y? Steps to evaluate a derivative implicitly 1) Differentiate both sides of the equation with respect to x. (Remember that y is a function of x, so you will have to use the chain rule.) 2) Collect all terms involving 3) Factor out the #4 #16 #28 dy on one side, and all others on the other side. dx dy and solve for it by dividing. dx Of course, your variables do not have to be y and x as seen in the next examples. #30 #42 Implicit differentiation is used to solve related rate problems. These are problems that show how fast one quantity is changing relative to another. Our variable will usually be t to represent time. When setting these problems up remember that the rate of change of a variable is given by its derivative with respect to time. #50 #54