Live Free or π Hard

As it is the last topic for the last quarter, I was expecting this concepts to be more challenging, but it wasn’t like that at all. Although it wasn’t that easy, I could say that I understood it faster than I thought. With this finished, all I have to do is prepare for the second long test, and I will already be set to a hopingly stress-free vacation.

I thought it would be the same with related rates, but it wasn't. It was confusing and I am usually clueless as to what equations to use, but somehow, I survived through it.

To be honest, I'm not sure if I'm doing things right. The rules on sketching in the previous Mathematics subjects have been easy to understand; however, the rules on sketching graphs using derivatives were confusing to me. To this point, I don't think I completely understand how to sketch graphs of functions using derivatives.

At first, I was not able to process the concept properly in my head. It really was confusing the first time I studied it, but it was actually pretty easy. All we had to do is apply what we had learned in the previous quarter.

Personally I found this topic easy to understand since it's about derivatives, which I understood properly from the previous quarter. I think I did better than before and now I should probably try to understand the concept of increasing and decreasing functions.

For this entry, we solved higher order derivatives, which is just like the previous problems but repetitive. In this topic, we applied all the previous topics we learned to solve the derivatives. In my opinion, since it is basically the same as the previous lessons, I think I did well in this topic.

The chain rule and implicit differentiation are both important because only by learning them do we make our understanding of derivatives deeper. Solving chain rule and implicit differentiation problems are similar to the other problems because we continuously apply what we learned in the previous problems. However, I think I'm still slightly confused whenever I solve implicit differentiation problems and the only way to resolve that is to continue practicing solving problems.

To solve the problem above, we use chain rule, rules on differentiation, and the derivative the inverse trigonometric function.

Solving for the derivatives of transcendental functions is important because it lets us have a deeper understanding of derivatives. For the past entries, we have been solving for derivatives; however, this time, the trigonometric and inverse trigonometric functions have their own unique derivatives. In my opinion, I still did well in this topic, although not as good as my performance in rules on differentiation. As always, I have to keep practicing solving for the derivatives of transcendental functions as it is the only way to improve my solving skills.

The rules on differentiation was an easy topic compared to the previous ones. It is important to learn this so that we can solve for the derivatives of functions more efficiently. This is the first time that I took on this topic, which is why it was very helpful. Doing the activities made me think that every rule is important to master as they could be combined to solve for the derivatives functions. In my opinion, I think I did well in these topics and I should now master each of them as they could be applied in the coming days.

Since the values and derivatives of both functions are already given, all we have to do is use the product rule.

Lastly, in item 3, we have to solve for the equation of the tangent line at (-1, -3/2). First, we solve for the derivative of the function as it is equal to the slope of the tangent line. By substitution, we would get the slope and use it along with the other given constants to solve for the value of b. With this, we can get the equation of the tangent line in the form 𝑦 = 𝑚𝑥 + 𝑏.

Getting the derivative of a function is basically the same as getting its tangent line. It is important that we learn this because it could be helpful in the coming lessons. In my opinion, I did well in this topic compared to the previous ones and the next thing I should do is to practice more on solving the derivatives of functions.

Checking if a function is discontinuous and getting the continuity of a function on an interval is a continuation of the last topic from the previous quarter. It is important to learn this so that we can identify the difference between continuity and differentiability. In my opinion, I did not do that well in these topics because of my shallow understanding of limits. As always, the only thing left to do is to keep practicing.

Just like the previous item, there is a jump essential discontinuity at 𝑥 = 1 since the limits as 𝑥 approaches 1 from the left and from the right are not equal.

Although I could never be totally confident, I think I understood these lessons easily. Finishing these series of lessons just means that I should prepare now to learn more and possibly harder mathematical concepts in the coming days.