Hyperbolic Functions. So....about hyperbolic functions...👀 They're not things that I have worked with a lot, however, they are similar enough to trigonometric functions that I don't feel too intimated to work with them. I've had the opportunity to work with them more this semester because of tutoring. So I though it would be fun to have them as part of this week's WMP!
To solve this week's problem in completion, you need to recall the following math skills:
✔️ Differentiation rules
✔️ Pythagorean identities
✔️ Factoring techniques
WMP! #27 wants us to...
Happy solving!
Check back on Friday, November 13th for the solution, which will be posted below ⬇️.
Shameless plug: Follow me on Instagram @TheYoungeLady
✏️📓 Solution Time! 📓✏️
⬇️
⬇️
⬇️
⬇️
⬇️
Differentiation time! The first thing I do is rewrite the function in a form that allows me to take the derivative more comfortably. What do I mean by that? Well, the second term in the function is rational, so one may be inclined to use the quotient rule to take its derivative. However, I am not so inclined. 🤫 I try to avoid the quotient rule whenever I can. 🤫
By rewriting the second term with a negative exponent, I can take the derivative of it using the power rule. Now, that that's complete, let's get to the taking the derivative of the function.
That's the derivative. It has been taken and simplified, ever so slightly, after applying the applicable differentiation rules. ...But I'm not going to leave my answer like this. Nope! There is more simplification that can be done. Here goes:
These are the kind of problems professors like to give. 👀 Let me tell you why. Are you 👂listening? Good. There was more work involved in simplifying the derivative compared to the work needed to find the derivative. In general, points are often lost in the simplification process. In my opinion, the differentiation process in this week's problem wasn't too bad. I or anyone could easily have made an error in the simplification process. How?
- By not knowing you can split the second term in the derivative up as a product of two factors, where one of them can be rewritten as a single hyperbolic function--tanh(x).
- By not knowing you could factor the derivative.
- By not knowing/being familiar with Pythagorean identities which allow for the derivative to be further simplified.
In a case like this, and lots of other problems, the algebra is where students make mistakes...not the calculus.
▪️ What is your relationship with hyperbolic functions like??
▪️ How did you do this week's problem??
▪️ Comment below with your responses and let me know what you thought about this week's problem.
Thanks for solving with me this week!
Up next...WMP! #28
😁➡️
Cheers!
The Younge Lady
No comments:
Post a Comment