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.
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!