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 was inspired by something mentioned on twitter and while it is not a difficult derivative, thinking about using the “not obvious” rule will help you look at functions in a new and different way. Try it out!
This week’s problem:
(click “see the solution” at the bottom of post to, well, see the solution.)
Find the derivative of using the product rule.
You can rewrite as . Normally, you would be totally right in saying “well, why would you do THAT?! You just made it more complicated!” but I was trying to find a way to write it as a product in order to use the product rule. Once you have rewritten it this way:
(I used the fact that is a constant so its derivative is zero)
Based on this, is its own derivative which makes sense since the slope of the “inside” function is 1.