*Sometimes easy and sometimes hard, our calculus problem of the week could come from any calculus topic. If you really want to get better at calculus, following these problems is a great way to make yourself practice! Past calculus problems of the week.*

**This week’s problem **

Find the derivative of using THREE DIFFERENT METHODS.

See the solution.

I will go through three of the more “obvious” approaches. If you found another way – please post!

Method 1: Simplify first.

Using the laws of exponents, . Therefore the derivative is (by the power rule)

Method 2: The quotient rule.

. It wasn’t pretty but it worked!

Method 3: The product rule.

First rewrite as a product: . Now:

.

PS you may have noticed that I used a slightly different way of writing out the product and quotient rules. While it is equivalent to the form you find in textbooks, I have always found this way easier to remember for myself and students!

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