*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
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
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: \[ f'(x) = 12x^2 + 2 \]
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.
I tried to calculate the anti derivative 💀 using power rule, realized my mistake 3 seconds in and solved it this also my sound weird but I’m in 8th grade
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 🥹
![Why you didn't learn tetration in school[Tetration]](http://i.ytimg.com/vi/Ea1_1aVfwl4/mqdefault.jpg)
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
More calc please! I could use the review🙌
agreed
*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
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.
@@sethcamargo1928
I've only made it to the area of a circle. But I'm starting to learn :)
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
this is easy, especially the way you explain it. thank you!
Very easy question bring some harder questions.
You’re the goat bro thanks
Hardest American calculus course:
You after posting this comment: 🤓
All calculus 1 courses start with these things. It even says "First time doing calculus." Wtf is wrong with you? Oh, nevermind. You're the ceo of "🤓"
@@Sh4dowbanned bro got worked up by a joke
@@Sh4dowbanned 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?
I used to miss this problem a lot but now I completely understand the break down.
Thank you for this explanation. Been struggling to understand this.
I know the answer very well its pretty easy, but man, take me back to algebra its so much fun
Thanks man!!!
👌👌 nice
I love derivatives, prob my favourite thing in math
Anti-derivatives would like to integrate you today.
@@maxpopkov1432😂 noice
I love integrals
Good ☺️
Wow very interesting!
Great vid!
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:
\[
f'(x) = 12x^2 + 2
\]
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.
Thanks a lot for this. It was very helpful
I've never heard the word decrement before. I'm going to start using it.
Guess you can say it derives from increment
Thank you ❤❤❤
Take me back to algebra is so real 🙏
Thanks sir 🙏💯
Take me back to algebra
thank you ❤️❤️
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?💀
As a Egyptian grade 8th student this is a piece of cake
They teach differentiation In grade 8?
Doubt
Cool 😎 🆒️ 😎 🆒️
Meanwhile the 8th Grade Indian Kid:
It says intro to polynomials.
@@gigguko6214basic calculus
Taking derivatives OF polynomials
Not the same thing
I tried to calculate the anti derivative 💀 using power rule, realized my mistake 3 seconds in and solved it this also my sound weird but I’m in 8th grade
I get the joke but for all foreigners calculus is only taught in class 11 & 12.
@@zerohzSame in India as well
Got main maths exam tomorrow😂
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.
Thank you i really like you 😊
omfg this saved my life i tried figuring out differentiability without learning this beforehand and boy was it confusing
Can it be solved according to the laws of short multiplication? like. (a-b)^=^a^+2ab-b.
Yes or no
Definitely going with D on this one 💀
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.
Applying the formula in nx power n-1
C.12x^2+2
D. Take me back to algebra
C. Thanks sir 🙏💯
C
cc thanks sir 🙏💯
Thanks mannn
Nice
12x2+2
after diffe i wish all math was this easy
How the concept happen...it just like memorise only.
Excuse me, what book are the examples taken from?
Just take me back to algebra pls😢
What are you using as a question provider.
And now use epsilon delta definitivion of limit to prove your result
It’s called the power rule right? Please state that
I remember the way to do most of these math questions youtube is recommending me but this was not one of them lol
This is pretty easy
Answer C power rule differentiation
Bruh you helped me pass the school test 😂THANK YOU ❤😊
A)f(x)=x^3 /3 +3x
Tq sar
Cc thanks sir 🙏💯 ever
Please take your
time and teach
Jee advanced toughest question ever💀
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
❤❤
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 so ez I did this fn just by reviewing the formula that it matched my ideas with
I would pick D
Like it
12x^3+2
I did that too
f(x)=x-8x+15
Man, even calc 1 students would find this easy.
Yeah obviously this is like the most basic thing in calc lmao
He wrote the 4 like a 9 and my attention slope dropped.
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
We learn it in 12th grade in Türkiye 🇹🇷
Easiest question
Option (D)
Algebra in 6th standerd:-😃. Algebra in 11and 12th:-💀
I just failed the exam about derivatives and this video shows up 💀
Was it hard? What part did you fail?
Me want to know pls
@@Sh4dowbanned bruh calculus is not impossible
And derivatives are pretty easy
Me too😢
@@keshavedits38 maybe it wasn’t taught well to them
Bro so easy
I got it right before the answer appeared!!! ❤❤❤
this is such an easy question
Only if you have been taught calculus!
Letter C
In one second I knew it was C
Letter choice D for me!
it becomes 0 because actually
+1=+1X⁰
+1.0X-¹
0
Choice D.. Take me back to Algebra. 🤣
I did this is my 10th grade
the 50 other derivative rules in question
Im in grade 8th but for being the basic staff calculus doesnt seem that hard
In India we do this I 9th grade
How 3 -1 from where
Have he choose B?
My schools teachers would get embarassed if such questions came in exam.
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 choose D
D
take me baaaaaaack
جزاكم الله خيرا صدق
What i didn't know that calculus have derivative !!! I take it in 12th grade
Diss eminem = song about u 🤠✌️❣️