Self-teaching calculus

Give me an example of something you can't understand intuitively.

d/dx[f(x)^g(x)]= a whole bunch of nonsense, at least to me

What are you talking about?

I taught myself derivatives when I was 15 and I could eventually intuitively understand it.

Go ahead a try me. I'll prove that my understanding goes beyond that.

>spend entire adolescence reading philosophy, essays, history, and technical documents along with math/cs/infosci
>fail first-year english two (2) times because i never learned to write a good-enough rough draft and edit it later
Just end my life homie
I'm never gonna make it. I'll learn a trade and parttime math classes until they kick me out.

[math] \frac{d}{dx}f(x)^{g(x)} = \frac{d}{dx} \left(e^{ln(f(x))} \right)^{g(x)} = \frac{d}{dx} e^{g(x)ln(f(x))} [/math]
Now notice that if you define [math] h(x) = g(x)ln(f(x)) [/math] then that last thing is literally the composition of the exponential function with h. In other words, [math] exp(h(x)) [/math]. And you understand the chain rule right? So the last thing equals
[math] e^{h(x)} \frac{d}{dx}(h(x)) [/math] and then finding the derivative of h is no more than an application of the product rule and then the chain rule again.

protip: it's just a meme, senpai

SO

APOSTOL OR SPIVAK?

I'm engineer but I want to git gud, but not mathematician-like gud

This just further proves that I'm a brainlet.
There was no external knowledge required for this, just applying what I already know.
Thanks anyway.

Neither then. Stewart.

There should honestly be some difficulty moving from algebra to calculus. You can't truly master a concept until you move past it, which is why the transition from algebra to calculus is so rough.

Most books assume you have an excellent understanding of algebraic manipulation and the average calc student doesn't, which is exactly what causes failure. Brush up on some rules. If you see algebra you're not sure of, ask. If you use it - look it up and right the full rule down. Chug out hundreds of derivatives (the "harder" ones like chain rule, quotient, product, etc.) and integrals (don't memorize inverse trig intervals at first - Prove to yourself why something is that with trig substitution). When you're done with this you should feel confident until series knee you in the balls, and then multivariable calc is easy (albeit, it involves learning more algebra you may not have seen before)

...

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>Be studying mathematical logic
>Solve pleb-tier problems
>Problem 40 appears:
>Prove that if [math]\Gamma[/math] is a tautology then there is a finite subset [math]\Delta \subseteq \Gamma[/math] such that [math]\Gamma[/math] is a tautology
>Two days and still cannot solve it

if gamma is a tautology then gamma is a tautology

no prove needed

btw how on earth can a set be a tautology?

Can I do Calculus or Computer Science with average intelligence/IQ?

Have other brainlets here walked said path and been successful with it?

Yeah, I failed that, at 3rd grade then succeeded in 4th hahahahaha. Fucking brainlets.

I got an A in all of the following: calc 1-3, DE's, intro to proofs, intro abstract algebra, linear algebra, applications of linear algebra, special functions, complex analysis...
and I've actually never seen or used the general form of that, lol

>no prove needed
My mistake. The problem is
>Prove that if [math]\Gamma[/math] is a tautology then there is a finite subset [math]\Delta \subseteq \Gamma[/math] such that [math]\Delta[/math] is a tautology

>how on earth can a set be a tautology?
Is a definition: a set [math]\Gamma[/math] of formulas is called a tautology if for every truth assignment [math]\phi[/math], there is at least one formula [math]A \in \Gamma[/math] such that [math]\phi (A) = T[/math] (true).

I've always been shitty with people but good at academics, every time I improve on a skill I want to talk to someone about it but I'm a neet

Am I even a brainlet (probably not I'm retarded) if I can't figure out how to talk to people

Since gamma contains one formula A that is always true ( A is a tautology ) you can always make a subset delta with this element.

For example: the singleton set containing A

Emotional iq != iq, but chads will surpass you. if you're attractive you'll do better but not having social skills still sucks, desu. I'm attractive (literally - I constantly get told) and moderately intelligent (have my degree in and work as EE), but have no social skills. People lose interest or avoid me after I spaghetti them for a few weeks. I think I probably come off as condescending

you are using what you want to prove, that it contains 1 tautology

consider something like an infinite chain of implications

f_i = f_{i+1} is true

and imagine this was a tautology, then the proposition you want to prove is false. but this can't be a tautology, why? what makes a tautology always contain finite "loops" and such?

>get a rudin thinking im smart and shit
have to start with stewart anyway

Aah well I read the definition wrong.

Better anwser: take as delta gamma. gamma is a subset of gamma QED

gamma need not be finite...

lim as x->1 of (x^3 - 1) / (x-1) ?

protip: no one here would say real talk so calm down my man

You should have Rudin alongside a calculus book

dumbass here, keep struggling to learn it and eventually you will get it

When I struggle with something in a math textbook it's often because I didn't care enough for the basics, so my advice to you is to go back to the beginning and make sure you understand the basics before moving on. If you don't understand something, don't skip over it. Divide and conquer.

What's a good book for studying mathemtical logic.
Also what if a tautology is constructed such that a formula is true only for a unique truth assignment, and every truth assignement is satisfied by that tautology.

3blue1brown released a new series about calculus on par with the famous linear algebra series. Go watch it

>taking calculus
>Don't really understand anything during lectures
>do badly on first mid term
>start self studying and stop going to lectures
>start getting full points on all assignments
>do well at final
Feels good not being a brainlet man.

I know branlet is a meme, but it's absolutely true. No matter how hard I try, I am dumb. That's not easy to admit.

That series is not that impressive when you realize that everything he is teaching "intuitively" is taught exactly the same in a pure mathematics calculus class and you even get the tools to be prove all of it rigorously.

I remember when taking Calc 1 the only thing that was not properly explained was implicit differentiation and that was because at the time the professor said we are already too tight on the schedule so we needed to move a bit faster.

not the OP but is it 3? I'm learning limits aswell

>final sem at uni
>gotta do inorganic course
>bored as fuck
>never study

>dad never loved me
>well at least I'm good at math
suicidepreventionlifeline.org/

I did fuckall in high school, used a TI-89 on the math placement exam and got into calculus and intro CS my first semester of college. I fucking died in calc since I didn't know how exponents worked but did a fuckton of problems and passed with a B

This semester i took linear algebra, physics 2 and physics 3. I completely failed. I couldn't handle it. I did try but it was just too much for me. The physics test where always on the same day or 2 days apart and it was impossible for me to multi task. Am I just not cut out for STEM? My major is comp sci but after this I'm thinking of quiting. I'm just so depressed and have lost all self esteem.

Try LONGER not HARDER. It will come to you user, just submerge yourself in the culture (shitposting here is a good start) and you will eventually become MORE BRAINLET THAN BRAINLET.

youtube.com/watch?v=E0E0ynyIUsg

>Implying I need my dad to love me when I can do analytic number theory

Missed A in Zorich's class by two points. Now he will never notice me.

Real talk. His protip was actually good.

reply only if your uni has fewer than 10 Nobel laureates

(((nobel)))

>nobelprize.org/nobel_prizes/literature/laureates/2016/

Obviously only talking about science