Finding the Derivative of a Polynomial Function | Intro to Calculus #shorts #math #maths

[cjlance_coconut]

More calc please! I could use the review🙌

[pedrobizondania]

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

[duggirambabu]

*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

[abbieamavi]

this is easy, especially the way you explain it. thank you!

[geraldtowler]

I used to miss this problem a lot but now I completely understand the break down.

[abhijeetbharti]

Very easy question bring some harder questions.

[atinybruh]

I love derivatives, prob my favourite thing in math

[zeetronn]

I know the answer very well its pretty easy, but man, take me back to algebra its so much fun

[bodesshorts]

As a Egyptian grade 8th student this is a piece of cake

[Kurzgesagt_fan]

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:

\[
f'(x) = 12x^2 + 2
\]

[ajae]

Thank you for this explanation. Been struggling to understand this.

[Vengeance]

Why am I getting recommended this, I'm in algebra 1 💀

[somebody_]

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.

[exiledfrommyself]

I've never heard the word decrement before. I'm going to start using it.

[thebluecreeper]

I started doing calculus at 11 years old and you are helping me a lot so far :D

[badribishaldas]

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)

[-ClerzZ-]

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.

[leann]

Thanks a lot for this. It was very helpful

[yennako]

omfg this saved my life i tried figuring out differentiability without learning this beforehand and boy was it confusing

[norastars]

Can it be solved according to the laws of short multiplication? like. (a-b)^=^a^+2ab-b.
Yes or no