Instantaneous Velocity, Definition of Derivative

[hibiscusenigma]

Hi

This is my approach.
Assuming the following:
1. the first derivative of an equation is the slope, velocity, density, price rate
2. the equalities p´ = dy/dx = Δy/Δx
3. when an object is at rest, there is no movement so velocity is zero
4. derivative is the ratio of a very very very small y and a very very very small x (instantaneous change so the use of d is favored over Δ because Δ is can either be big or instantaneous)

By assumption 1, we derive the equation by following the power rule
p=t^2-6t+8
p´ = dy/dx = Δy/Δx = 2t-6

2t- 6 is our velocity and we are given another velocity which is 30 m/sec so we can plug it in our Δy/Δx or dy/dx (assumption 4),
30=2t-6
(30+6)/2=t
18=t

By assumption no. 3,
velocity is zero when the object is at rest therefore,

p´ = dy/dx = Δy/Δx = 0 = 2t-6
0 = 2t-6
6/2=t
3=t

[Pallen]

Thank you so much for taking the time and demonstrating the definition of a derivative! This video will be eternally useful and I am grateful.

[heliscat]

I finally understand why the "h" vanishes! I have a not so good instructor.Thank you!

[ishakhalid]

thanks very helpful, i needed a video using the longer method because that is what I am being tested on

[Diomedsspear]

In the beginning you said "60 meters per second" on accident instead of 30 meters per second. Might want to add a little note there correcting that. Great video btw! :D

[markreza]

Thank you for breaking it down step by step!

[patrickjmt]

@KamDaug i honestly don't see the point in your complaining.

[jalipenorunner]

my fav tutor on youtube tho. thanks man!

[Scuber-cdzl]

You are the best dude. I mean it's so clear now..

[rounakshaw]

repeated twice
but it doesn't matter
a human can do mistakes
and Mr. PJMT is great

[brandongregory]

Why use limits to find velocity, from the position vector, when you can just take the first derivative of the equation? or is taking the first derivative wrong in some case's? or are they the same thing?

[AnandRaiSays]

you sir are a LIFE SAVER!!!! . Keep the good work up
:D

[SoSerendipitous]

This just blew my mind. I've literally never understood the limit definition of the first derivative ever until right now; thank you so much!!!!

[tsegazabzewdu]

Bro that was so helpful thank you so much!!

[harshdeepall]

nice tutorial, but why do it using lim as h approaches 0, whn u can just multiply the power by the coefficient and take 1 away from the power, and do the same for the whole eqn and there u have it, ur first derivative. eg. f(x) = 4t^3 + 3t + 4, f ' (x) = 12t^2 + 3. Alot easier :P.

[patrickjmt]

@calbright12 cause it stops, and then it starts moving again. why is that not possible?

[buhnhi]

why did he find the derivative the long way?

[justbibi]

why in the last video you just get the derivative of the given number to get velocity while here, you have to get the limit to get the velocity? when will i know if whether should i get the limit or derivative of the given in getting the velocity?

[luvdy]

Can I ask what is the instantaneous acceleration in that equation

[rusul]

Can you do more videos about chain rule please ur videos are very helpful