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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✏️📓 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