I need help with understanding differential calculus

[dense solar]

I understand how to find the area under the curve but I don’t understand most of the other stuff I can’t find any good courses online so could I get help?
(Sorry if I said this aggressively or if y’all thought I was being rude)

[ionic sphinx]

go to khan academy

and get a book

[obsidian ocean]

show a problem you need help with

[pliant vessel]

Hey man I can help you understanding

So, have you already studied limits?

$\lim_{x \to a} f(x)$

[indigo patio]

rojan

[dense solar]

Yes, sorry I was at school. I need help understanding derivatives although I know how to find the area under the curve I still need help understanding. BTW thanks for reaching out!

[pliant vessel]

Alright, im here

do you prefer here or in your dm?

[dense solar]

Idc

I can do whatever

[smoky sequoia]

Typically you learn derivatives before learning integrals

Was this ever resolved?

[dense solar]

Yes, but my older brother taught how to find it like a month ago.

[smoky sequoia]

Find what?

[pliant vessel]

@dense solar Hey

So, about derivatives

Imagine a ball rolling down a slope. Newton saw it falling many times and started to think about the speed of the ball, he realised the ball got faster with time, in other words, the ball speed varied

Just like speed is the variation of position, aceleration is the variation of speed

[smoky sequoia]

True, now how would you explain integration?

[pliant vessel]

I'm not explaining integration yet

although you do not necessarily need to know derivatives to understand the concept of integration

[smoky sequoia]

Nope, not at all, lol. Here's how I would explain it. Consider the velocity of the ball at a specific time, t. Over an incredibly small time interval dt, the ball travels a distance v(t) * dt. Now, if we consider all the tiny distances traveled as time changes, and we add it all up (integrate them together,) we get the total distance traveled.

$\int d\vec{r}=\int \vec{v}dt=\Delta \vec{r}$

[indigo patio]

pebble

[smoky sequoia]

And notice that from this, if you drop the integral, you get

dr = vdt,

dr/dt = v

r being the position

Hope that makes sense

[pliant vessel]

. . .

[smoky sequoia]

??