Weekly Math Problem #78

2nd Derivative. If you're anything like me, then you may treat finding the derivative of a function like solving a puzzle. I find a lot of puzzles fun...until I get annoyed at how long it takes me to do it, if it's taking me too long. 🙄 Typically, finding the first derivative of function is not too bad. Finding the higher order derivatives is where some of the challenge may come in. This depends on what type of function the previous derivative yields. This week, we'll just go up to the second derivative. (If you want to go higher, let me know.)

To solve this week's problem in completion, you need to recall the following math skills and information:

       ✔️     Differentiation rules
       ✔️     How to find a derivative

            

WMP #78 says ...

Happy solving!

Check back on Saturday, April 2nd for the solution, which will be posted below ⬇️.

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Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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Here we go. If you remember how derivatives work, then you'll remember that you have to find the first derivative before finding the second derivative. So let's do that. To find the first derivative of the function, the product rule is required.

Applying the product rule to h(x) is as follows:

Now that we've found the first derivative, we can find the second derivative...which is that the problem asked us to find. The first derivative consists of two terms--each needing the product rule to find its individual derivative. I use a green plus sign "+" to show the two terms, and their respective product rules are below their respective  diagonal arrows.

After applying the product rule twice on the first derivative and combining like terms, we have the second derivative, h''(x). 

 

▪️ Did you get the same answer for your second derivative?

▪️ Let me know what you thought about this week's problem in the comments section. 

Thank you for solving with me this week. ✏️
We're on to WMP! #79. 🤓

Cheers!

The Younge Lady

It's My 2nd Blogiversary!

 

YAY! It has officially been 2 years since I published my first blog post. If you haven't read it, you can read it here: Who's That Lady?! You're welcome.☺️ Time is going by faster than I thought. From Monday, January 20, 2020....and now we're here...Thursday, January 20, 2022.🤯 After 2 years, I'm still glad that I created this blog. 🙌🏿 

Last year (First Blogiversary), I created a word search puzzle using some words associated with my blog. This year, I decided to stick with the puzzle theme. This year we have a crossword puzzle. 

 2nd Blogiversary Puzzle! PDF

Happy cross-wording!

Your support is still appreciated and that's not going to change! Thank you for...
        ✔️ clicking the link
        ✔️ reading the blog posts
        ✔️ solving with me 
        ✔️ following me on Instagram
        ✔️ liking and commenting 
I'm grateful!

I haven't done any videos yet, but I haven't given up on that; it's still on my mind. I'm going with the ebb and flow of my life, working out the right time to make it happen. Share your thoughts below ⬇️.

Shameless 🔌 Plug:  Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee:  TheYoungeLady ( I'm gonna need it this year. 😆 )

Cheers!

The Younge Lady

Weekly Math Problem! #47

2nd Order ODE. Sometimes, topics just come to mind and I say to myself, 🤔 "Haven't done that in a while. I should do it so I don't forget." That's pretty much it. Well, sometimes I can see the problem or parts of the problem and not quite remember the name of the topic. Then I'll have a little digging to do so that I can get the name of the topic. Well, 2nd order ode (second order ordinary differential equation) is the order for this week. 😅 Specifically, we're looking at a non-homogenous equation with constant coefficients.

⚠️Many steps involved.⚠️To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to factor a trinomial
        ✔️     How to use the method of undetermined coefficients
        ✔️     How to find derivatives

WMP! #47 says to:

Happy solving!

Check back on Friday, April 23rd for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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You can't say I didn't warn you about the many steps involved in the solution to this problem. Why did I do it? Well...because it's good practice and I want to make sure that I can remember math at this level. As I challenge my myself, I challenge you. 

🧐 Let's get it!

I did my best to organize my solution and color code it so that it would be understood a little better.

The general solution to the equation can be broken down into two parts--the homogeneous solution and the particular solution.

I worked on the homogenous solution, before tackling the particular solution. Once I got bot parts, I put them together to complete the general solution to the equation.

This one was quite a bit of work but, it got done! 🤔 I think I'll do another one like this sooner than later. 

▪️ Have you ever encountered this kind of problem when learning about differential equations?

▪️ Leave your responses down below and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Up next, WMP! #48. 👩🏿‍🏫

Cheers!

The Younge Lady