1. 3.6 Implicit Differentiation And Rational Exponents

2. Rational Exponents are easy! These problems will have exponents that aren’t integers; they will most likely be fractions. Hmmm… how could an exponent be a fraction?? That’s right! A radical!! It doesn’t matter. You will still use the generalized power rule:

3. Examples 1.Find if 2.Find if Functions do NOT need to be rationalized; only numbers need to be rationalized.

4. Implicit Differentiation This process is used when y cannot be isolated. We will look at a problem where y CAN be isolated to understand the idea, but in many problems y will be mixed in as a product or a quotient. We will be treating y as a differentiable functions.

5. Let’s try this one Same thing right? The derivative of y in terms of x has to have that extra symbol because “y” is not “x”

6. What does this mean? WHENEVER you have to take a derivative of y, tack on. No kidding. Then, isolate. There might be y in your answer; it also might be easy to sub back in y. Lets see an example… or two….

7. Examples 3. Find if 4.Find if 5.Find if (hint: continue #4) Leave y in the answer.

8. Examples 6. Find the slope at (-1, 1) for