I just finished calculus 3, and yeah, what you learn in calculus 1 become very easy after go through enough pain, suffering and doubt. Don't give up people, im really not that smart and managed to survive
I love that you have to make it to calc 3 to figure out where the volume eq for a sphere comes from. Felt satisfying doing a triple integral for a unit sphere.
They have to teach you all different types of calculus just till u get a phd when they tell you how to create your own math and then realize all math is made up
*Formulae:* 1). If f(x) = xⁿ then f¹(x) = nxⁿ⁻¹ 2). If f(x) = x then f¹(x) = 1 3). If f(x) = k then f¹(x) = 0 where k is a constant If f(x) = 4x³ + 2x - 1 then f¹(x) = 4 * 3x² + 2 * 1 - 0 = 12x² + 2
@Mike First time doing calc has much more preparation for derivatives using limits and eventually teaching the definition of a derivative. There's also continuity, asymptotes, etc and Simply teaching power doesn't help people understand why it works.
@@creativelad3680 It was in a suburb near Dallas, It was part of my Pre-AP algebra class and more of just an intro where we learned the differentiation rules and did some basic applications. We also took the PSAT in that class and if we scored high enough we could be exempt from taking our SATs and ACT in high school!
Answer choices A and B can be eliminated because the derivative of the first term of f(x), 4x^3, is 12x^2 by the Power Rule. Since only answer choice C has 12x^2 for the first term of f’(x), C is the final answer. This is basically easy-level calculus. Things get more complicated as you go on.
To calculate the derivative \( f'(x) \) of the function \( f(x) = 4x^3 + 2x - 1 \), we'll apply the basic rules of differentiation. Specifically, we will use the power rule and the constant rule. 1. **Differentiate \(4x^3\):** The power rule states that if \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \). For \( 4x^3 \): \[ \frac{d}{dx}(4x^3) = 4 \cdot \frac{d}{dx}(x^3) = 4 \cdot 3x^{3-1} = 12x^2 \] 2. **Differentiate \(2x\):** Again, using the power rule: \[ \frac{d}{dx}(2x) = 2 \cdot \frac{d}{dx}(x) = 2 \cdot 1 = 2 \] 3. **Differentiate \(-1\):** The constant rule states that the derivative of a constant is zero: \[ \frac{d}{dx}(-1) = 0 \] Now, combine the results of each term: \[ f'(x) = 12x^2 + 2 + 0 \] Therefore, the derivative \( f'(x) \) of the function \( f(x) = 4x^3 + 2x - 1 \) is: \[ f'(x) = 12x^2 + 2 \]
I just took psats and haven’t gotten to calc yet, a question was similar on here, glad to know that this is simple and now I know for the future. Thanks man 👊 and keep the good work. These are really simple and helpful.
Yes now calculate the Gradient of the Potential energy Function to Find the Work done when an Object traverses in a Black Hole Under Conservative and Non Conservative forces. And assume the Non Conservative forces are Air Friction and have minimalist effect on the Internal Potential Energy. U = 3XY/(X+Y) x arctan(cos³x^y)
This is calculus? I’m taking this rn in my college algebra class. The last time I took algebra was over 5 years ago and never seen these before… makes sense now. But don’t know why they would put calculus in an introductory algebra course 🥹
Take me back to algebra 😭😭😭
Lmao good luck with college math classes 💀
@@Salza02multiplying and subtracting oh GOD 😪😫
This is basic 💀
@@Salza02 not just math also PHYSICS
it's not that bad I'm in 9th grade and I've learned integral and derivative calculus, it just takes time and repetition
More calc please! I could use the review🙌
agreed
U need to study ur notes from teacher
I just finished calculus 3, and yeah, what you learn in calculus 1 become very easy after go through enough pain, suffering and doubt. Don't give up people, im really not that smart and managed to survive
I love that you have to make it to calc 3 to figure out where the volume eq for a sphere comes from. Felt satisfying doing a triple integral for a unit sphere.
What references are you using? please kindly share
I assume you also work hard as fuck
They have to teach you all different types of calculus just till u get a phd when they tell you how to create your own math and then realize all math is made up
*Formulae:*
1). If f(x) = xⁿ then f¹(x) = nxⁿ⁻¹
2). If f(x) = x then f¹(x) = 1
3). If f(x) = k then f¹(x) = 0 where k is a constant
If f(x) = 4x³ + 2x - 1 then
f¹(x) = 4 * 3x² + 2 * 1 - 0
= 12x² + 2
But how were these formulae found?
@@wasordx3245 why don't you google, the OP probably doesn't know
@@neutronzz3543 Google ain't helpin gonna ask the GPT
@@wasordx3245jeremy klassen
Both 2 and 3 follow from 1 and are pointless to write
this is easy, especially the way you explain it. thank you!
Hardest American calculus course:
You after posting this comment: 🤓
@Mike bro got worked up by a joke
@Mike bro got worked up by a joke
Buddy the caption says "Intro to Calculus." Do you expect him to be doing Taylor series or some shit?
@Mike First time doing calc has much more preparation for derivatives using limits and eventually teaching the definition of a derivative. There's also continuity, asymptotes, etc and Simply teaching power doesn't help people understand why it works.
I used to miss this problem a lot but now I completely understand the break down.
I love derivatives, prob my favourite thing in math
Anti-derivatives would like to integrate you today.
@@maxpopkov1432😂 noice
I love integrals
You’re the goat bro thanks
Very easy question bring some harder questions.
Thanks for easily teach....
I know the answer very well its pretty easy, but man, take me back to algebra its so much fun
Thank you for this explanation. Been struggling to understand this.
I've never heard the word decrement before. I'm going to start using it.
Guess you can say it derives from increment
Wow very interesting!
Take me back to algebra is so real 🙏
Nice!
👌👌 nice
Why am I getting recommended this, I'm in algebra 1 💀
It preparing you for the future.
I'm in abstract algebra lmao
It's not algebra imao
Because it’s easy
Which grade in America are you?💀
I started doing calculus at 11 years old and you are helping me a lot so far :D
Okay Mr. Boy genius
@@peterk.2108 thank you
Good ☺️
As a Egyptian grade 8th student this is a piece of cake
They teach differentiation In grade 8?
Doubt
@@creativelad3680 They teach differentiation in 8th grade in Texas too
@@dingus6317 where ?
I haven't really heard of that
Also do they just dump formulas or teach u core of calc
@@creativelad3680 It was in a suburb near Dallas, It was part of my Pre-AP algebra class and more of just an intro where we learned the differentiation rules and did some basic applications. We also took the PSAT in that class and if we scored high enough we could be exempt from taking our SATs and ACT in high school!
@@dingus6317 I guess one could say power rule is like 8th grade
Anything more that power rule can be over 8th grade tho
Thanks man!!!
Answer choices A and B can be eliminated because the derivative of the first term of f(x), 4x^3, is 12x^2 by the Power Rule. Since only answer choice C has 12x^2 for the first term of f’(x), C is the final answer.
This is basically easy-level calculus. Things get more complicated as you go on.
omfg this saved my life i tried figuring out differentiability without learning this beforehand and boy was it confusing
Thanks a lot for this. It was very helpful
This is cool
❤ Option (D)
I'd love this.
Take me back to algebra
To calculate the derivative \( f'(x) \) of the function \( f(x) = 4x^3 + 2x - 1 \), we'll apply the basic rules of differentiation. Specifically, we will use the power rule and the constant rule.
1. **Differentiate \(4x^3\):**
The power rule states that if \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \).
For \( 4x^3 \):
\[
\frac{d}{dx}(4x^3) = 4 \cdot \frac{d}{dx}(x^3) = 4 \cdot 3x^{3-1} = 12x^2
\]
2. **Differentiate \(2x\):**
Again, using the power rule:
\[
\frac{d}{dx}(2x) = 2 \cdot \frac{d}{dx}(x) = 2 \cdot 1 = 2
\]
3. **Differentiate \(-1\):**
The constant rule states that the derivative of a constant is zero:
\[
\frac{d}{dx}(-1) = 0
\]
Now, combine the results of each term:
\[
f'(x) = 12x^2 + 2 + 0
\]
Therefore, the derivative \( f'(x) \) of the function \( f(x) = 4x^3 + 2x - 1 \) is:
\[
f'(x) = 12x^2 + 2
\]
B
Cool 😎 🆒️ 😎 🆒️
I would pick D
There is an easy formular to figure these out in a second. If it was by first principles, it would be more difficult but it's not.
Great vid!
How the concept happen...it just like memorise only.
Could you please slow down a bit ❤❤❤❤❤
I just took psats and haven’t gotten to calc yet, a question was similar on here, glad to know that this is simple and now I know for the future. Thanks man 👊 and keep the good work. These are really simple and helpful.
C.12x^2+2
after diffe i wish all math was this easy
12x2+2
Definitely going with D on this one 💀
Bruh you helped me pass the school test 😂THANK YOU ❤😊
As a Korean 7th grader, it is too easy problem😂
I already learned all Korean math curriculums.
C
This is pretty easy
Thank you ❤❤❤
A)f(x)=x^3 /3 +3x
And now use epsilon delta definitivion of limit to prove your result
Thanks sir 🙏💯
Yes now calculate the Gradient of the Potential energy Function to Find the Work done when an Object traverses in a Black Hole Under Conservative and Non Conservative forces. And assume the Non Conservative forces are Air Friction and have minimalist effect on the Internal Potential Energy.
U = 3XY/(X+Y) x arctan(cos³x^y)
Air friction in a black hole XD
There is no potential function when the force field is non-conservative.
this is such an easy question
Only if you have been taught calculus!
Thank you i really like you 😊
Please take your
time and teach
f(x)=x-8x+15
This is calculus? I’m taking this rn in my college algebra class. The last time I took algebra was over 5 years ago and never seen these before… makes sense now. But don’t know why they would put calculus in an introductory algebra course 🥹
I just failed the exam about derivatives and this video shows up 💀
@Mike bruh calculus is not impossible
And derivatives are pretty easy
Me too😢
@@keshavedits38 maybe it wasn’t taught well to them
Man, even calc 1 students would find this easy.
Yeah obviously this is like the most basic thing in calc lmao
D. Take me back to algebra
I remember the way to do most of these math questions youtube is recommending me but this was not one of them lol
C. Thanks sir 🙏💯
This is so ez I did this fn just by reviewing the formula that it matched my ideas with
a constant is actually just the same as: (the constant) * x^0 so when you differentiate cx^0 you just end up multiplying by 0 -> 0*c*x^-1
12x^3+2
it becomes 0 because actually
+1=+1X⁰
+1.0X-¹
0
Hmm sir why the -1 became +0?
Can you explain it here in the comment?
Nice teaching i understand it under a min thx
-1
x⁰=1
So -1x⁰=-1
Use power rule
0×-1/x
Which is just 0
❤❤
Just take me back to algebra pls😢
Applying the formula in nx power n-1
He wrote the 4 like a 9 and my attention slope dropped.
Can it be solved according to the laws of short multiplication? like. (a-b)^=^a^+2ab-b.
Yes or no
I recently completed 10th🥲🥲i wish I would this channel before
Nice
Answer C power rule differentiation
cc thanks sir 🙏💯
I got it right before the answer appeared!!! ❤❤❤
Thanks mannn
Algebra in 6th standerd:-😃. Algebra in 11and 12th:-💀
Letter C
Cc thanks sir 🙏💯 ever
Bro so easy
It’s called the power rule right? Please state that
In one second I knew it was C
Easiest question
I did that too
hardest quetion in america
Jee advanced toughest question ever💀
Option (D)
Tq sar
Letter choice D for me!
Like it
My schools teachers would get embarassed if such questions came in exam.
I did this is my 10th grade
D
What application are you using??
جزاكم الله خيرا صدق
We learn it in 12th grade in Türkiye 🇹🇷
Choice D.. Take me back to Algebra. 🤣
Just integrate the options if you are unable to find the derivative 💀
Usually it's easier to do it the other way around. It's very rare that it is easier to integrate than it is to find a derivative.
I choose D