Project: Logarithmic Differentiation

Section 7.4* - 15 Points

Due:

Let. As of now, none of the rules that we’ve learned seem to help us find f’(x)

1. Why can’t you use the Power Rule to compute: f’(x)?

2. Why can’t you use a formula like to compute f’(x)?

Method 1

3. Start with the equation . Take the logarithm of both sides to get . Then use a property of logarithms to help you find the derivative of

4. Now use implicit differentiation to find

5. Since , you can equate your answers in Parts 3 and 4. Do so, and then replace all y terms by .

6. Perform some algebra to get alone on the left hand side, and you are done with this method.!

Method 2

7. Let . What is the relationship between and ?

8. If , compute g’(x). What techniques are you using in this case?

9. Since you have done the same problem in two different ways, show that your answers to Problems 6 and 8 are identical.

10. Let y = f(x) be implicitly defined by . Compute y’ in terms of x and y. Hint: Can logarithms help you?