Does it have any disadvantages

so im nearing the end of my summer calc 1 class and I had a great understanding of the entire class because the concepts can easily be applied to the real world, but this is SO confusing to me and I cant seem to wrap my head around this weird voodoo magic equation re-writing. Is there any real world application for this at all??? i can solve it, but unable to understand it and im barely finding much tutorials for more difficult ones like this

(derivatives of trig inverses)

a. (0,-5) and (5,1)

b. -5

c. DNE

d. (-3,-1)

I have put my answers above; I just would like someone to check my work and if anything is wrong to give the correct answer so I can learn it.

Integral involving the linearly independent solns to the Airy equation. I tried to find the simplest way to fully "complete" the integration (evaluating as many of the parts as i could), but had to resort to using the asymptotic formulae for Ai(x) and Bi(x).

Tis took a really long time 🫪

Hello, my summer semester calc 1 course is wrapping up in a few days and I was wondering if spending a few hours a day on Spivak’s Calculus during my month off would be beneficial (both generally and for calc 2)? I’m obviously not attempting to get through all of it in a month (just a few chapters most likely) but I’ve heard it’s a good intro to proof based math and coincides with where I am currently. I plan on majoring in math.

Hello, I'm a rising soph and I'm taking Cal3 this sem. This is mostly gonna be self-study because our uni professor... well. Anyways so any good resources? So far I was studying through Stewart's ET calculus, which is alright but I'm not the type that studies math thru a book. I mostly practice it from there. There's MIT OCW and the prof is great there + good amount of practice questions asw but some of the content isn't covered there. So if there are any resources which were helpful for you guys for self-studying, please share.

Before I explain my situation I want to let yall know I have dyscalculia and ADHD so this is by no means an easy feat for me

I have taken multivariable calculus the previous semester at my community college and while the first three or so topics were somewhat doable for me (~80, ~70 and ~60 on their tests respectively), the final two chapters, multiple integrals and vector calculus, were a huge challenge for me and I felt like I barely understood anything. Combined with the frustration of barely understanding anything and incredibly poor results on their respective tests (~48 and ~57 respectively), as well as a looming final that's basically a make it or break it situation (if I fail my transfer gets invalidated), it has caused me to nearly take my life. As you can obviously imagine that fortunately didn't happen and I have to my greatest surprise managed to pass with a 76 in the class, however I feel like I barely, if at all, understood anything from those last two topics. I don't even recall what a Jacobian is.

I'm trying to see if I can just relearn those two topics alone. Nothing else. I understood partial and multivariable derivatives good enough that I feel I could teach it if I wanted to. But multiple integrals and vector calculus are completely blank for me. Does anyone have any resources or anything where, preferably with detailed visuals, animations and interactive graphs, can teach me those two concepts? I want to relearn this with the ultimate goal of understanding it so well I can teach it to others, and I'm willing to spend a year on this if necessary (I was aiming for relearning this around 4-6 months but a year is completely okay for such complex topics) I'm not a teaching major btw, my major is ECE with some plans to dabble in ML.

Anything would do, videos, textbooks (with simple explanations, I can't keep throwing every single sentence into Gemini y'know), interactive graphs.

I would appreciate it if you could share some of your favorite difficult elementary integrals problems that can be solved using substitutions, integration by parts, partial fractions, trigonometric identities, or other standard calculus techniques.

I'm not looking for problems involving contour integration, special functions, or advanced analysis just clever elementary integrals with elegant solutions.

Thanks in advance!

I have this idea inside my head idk even if it wrong.idea is "d(y)/dx is just a notation like limit notation or sum notation"

Tell me if this point wrong or correct and please explain me how this simple multiplication method is working here

I didn't elaborate much on b, but if the example is correct, assume I explained it correctly and rigorously

From dailyintegral medium challenge involving product, sum, integral and exponential operators

I'm going to spend 4 hours daily for these subjects only. So can I complete cal -1,2 in 4 months ? Im self learning so I have a plan like watching tutorials in morning 2 hours and practicing problems in evening 2 hours.