Here is the shortcut to do this: Step 1: Find the derivative of x²+1 Step 2: The Derivative is 2x Step 3: Plug X=3 into 2x, which would look like 2(3), and the answer will still be 6. Doing this will save a lot of time.
You can just solve without the numbers and do: (f(x+h) - f(x))/h = (x^2+2xh+h^2+1) - (x^2+1) = (2xh+h^2)/h = h(2x+h)/h =2x+h lim (h -> 0) = 2x + 0 = 2x *At that point you can just plug in the value (3) = 6.
+Sith Lord Its Called Tangent Line because the Slope of the Line "Touches" the Parabola or said Graphed Equation. (The Word Tangent is derived from the Latin Word "Tangens" which means "Touching")
I think because that would just give you the y-value, not the slope. So x would be 3 and when you plug it in, and get 6, which would be the y-value. So now you found the coordinates of the point (3,6)
chris freedman that certainly would be easier but this video is meant to help finding the derivative of a function by using the definition (instead of using the power rule).
rootmath but if u use the power rule---u still have to add on the 1-----(2(3)+1) would be the new equation---=7 instead of 6 ?????? could u pls explain?
can anyone help me... Find Points of intersection of the function y=x^3-3x^2+2x of the axes , i have no clue how to do this , i moved from a 4 point class to 5 point class in israel , and this makes no sense to me
Yeah, show them the hardwar. Dr Sylvanus P.Thompson wrote on the prologue of his book: ``Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics - and they are mostly clever fools - seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.''
Considering this is the first step in learning derivatives, I think it was well produced. People need to visualize a derivative before they move on to the rules.
Here is the shortcut to do this:
Step 1: Find the derivative of x²+1
Step 2: The Derivative is 2x
Step 3: Plug X=3 into 2x, which would look like 2(3), and the answer will still be 6.
Doing this will save a lot of time.
he's making use of the power rule, guys.
Kanye East thank you because this was much much simpler
7 years later and ur still a legend my dude
Thx!
time flies, you are all welcome!
I can't even properly express how helpful this was to me, thank you so much!!!
I agree, though this may not fully help me with Calc and Precalc I'm less likely to fail the class again this Fall Semester.
I was actually crying out of frustration before I found this video. Thank you!
This guy is amazing!!
@@wolframalpha8634 ikr
very useful 12 years later thanks mate
This is the only video that I've watched that actually helped me out.
I'm really happy it helped you!
from several years ago, yet still the only video on youtube that helped in the slightest
Google recommended me this video. Needless to say it definitely helped.
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your simplicity and patience while teaching is admirable thank you for this lesson
Me before watching this video (2:10)
Bruh I'm done 😂
Same 😂
Wildfire Studios me after watching this video
For any more complicated expressions, you may use L'hopitals rule, derive, and then plug in the value of x to find the slope of the tangent line
You can just solve without the numbers and do:
(f(x+h) - f(x))/h = (x^2+2xh+h^2+1) - (x^2+1)
= (2xh+h^2)/h
= h(2x+h)/h
=2x+h
lim (h -> 0) = 2x + 0
= 2x
*At that point you can just plug in the value (3) = 6.
i always confuse it but you really clearfied me thanks from djibouti
Great explanation, I was forgetting to substitute the f(3) into its own function as well.
Thank you so much man ,I have been struggling to figure out about differentiation, your video helped so much:)
It's both a shame and awesome that a 6 minute video can be so much more informative than a 70 minute lecture
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You should post some questions to work on after completing the video. That would be super helpful!
Thanks.
Thank you sooo much for this video!! You broke it down sooo well!! God bless you!!😊
Im sorry, when you expanded the first term, where did you get 6h from?
Factoring (3+h)^2 gives you 3(3) + 3h + 3h+ h(h), which is simplified to 9+6h+h^2
He made this video in the morning, because you can hear the birds chirping at the end of the video :)
Question; what kinda laptop / computer you using to write this on? Also great video!
RootMath, you're the real MVP!!!!
Dude, I can't thank you enough for making this. My gr12 functions teacher is so bad, and this helped me understand.
your patience while teaching is amazing may ALLAH bless u
This was really helpful, but how would you apply it to f(x)=x^3-3x^2+8x where x=2
Thanks I'm taking a five week mini course and this helped a lot
Does anyone know how he got 6h in the equation of distributing? that just kinda threw me off
See comment above, by NN .
Thanks this video helped me a lot. Much better than seein it in class!
Where did the six come from and why was there a new h?
Couldnt you just turn it into derivative form? So thats x^2 + 1 = 2x + 0. And at x = 3 : 2 x (3) + 0 = 6?
fizzyjizzz where can i learn this way?
fizzyjizzz that depends on your teacher, our teacher require us to derive it by using definition of derivative
Thank u for understand this topic, your the best 💗✨️
this video is so good i want to give you money
Well if you have a lot of money and want to make a donation to rootmath you can. ;) I'm glad this video helped you!
y = x^2 + 5x When x = 4 Is the Slope 13 or 9?????
+Ix Blind 2x+5=8+5=13.
This is late, but it came from foiling (3+h)², and once you broke it down it would look like (3+h)(3+h) and then you foil it.
Thanks NN., that’s what I was looking for. 😉
awesome video. thanks!
May the FSM bless you for your kindness.
this was really helpful for finals review!!!!
Great example and very nice, step by step!
what tools(software) you are using?
How do you find the slope without a function and only a given point?
so will the constant term always cancel out?
How do you know how long the tangent line is?
okay but what does the 6 mean???? is that the y-value when x is 3???
6 represents the slope of the tangent line
the y value when x is 3 would be (3)^2 + 1, so 10.
This was spectacular! Thank you!
can someone help me i dont know where the 6 came from when it was 9h +6h 3:15
same
Expand (3 + h)^2. You get
(3+h)(3+h) = 9 + 3h +3h + h^2
Add the two 3h terms to get 6h
@@rootmath ohhhhh thank you very much
ok... I just started on this unit, but why do they call it tangent line? I don't see any tan/cot function inputs?
+Sith Lord Its Called Tangent Line because the Slope of the Line "Touches" the Parabola or said Graphed Equation. (The Word Tangent is derived from the Latin Word "Tangens" which means "Touching")
oh my god this video really help me. thank you so much.
Wish my teacher posted videos like this!
Thank you so much this has been super helpful!!
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Thank you very much!! Very well explained.
Wait where does 9 + 6h + h² come from...Aw screw it I tried. Im just going to wing my test tomorrow xD thanks for the help though.
@Ammeer JT lmfao
Whats the point of writing the limiy?
Thanx a lot, u hv made it so easy for me
i know this is a stupid question but i'm lost on [(3+h)2+1] become 9 + 6h + h2 + 1?
khalid share haha thanks I thought I was crazy too
khalid share (a+b)^2=a^2+2ab+b^2
@N "or FOIL it!"
what if the value of x is not given?
I dont know why you wouldnt just do f '(x)= 2x and then just plug in the 3
I think because that would just give you the y-value, not the slope. So x would be 3 and when you plug it in, and get 6, which would be the y-value. So now you found the coordinates of the point (3,6)
chris freedman that certainly would be easier but this video is meant to help finding the derivative of a function by using the definition (instead of using the power rule).
rootmath but if u use the power rule---u still have to add on the 1-----(2(3)+1) would be the new equation---=7 instead of 6 ?????? could u pls explain?
+greg l That is because the f'(1)=0 so after you get f'(x^2+1) = 2x there fore f(3) = 6
Thank you, And Thank you again.
Wow, you’re amazing. Thank you
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You sir, are a genius!!! :D
3:17 how did he get 6h ?
thanks! this was very helpful!
Thanks. A confusing subject.
Thank you so much , now I understand 😭😭😭♥️♥️♥️
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can anyone help me...
Find Points of intersection of the function y=x^3-3x^2+2x
of the axes , i have no clue how to do this , i moved from a 4 point class to 5 point class in israel , and this makes no sense to me
how did he get the six
how did u get 6h
The slope is 6 what? What 6? WHat oes that mean?
Fantastic ---thank u Sir!
Very helpful thanks.
Where u get 6h
where does the 6h come from?
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Nice photo 😂. ( 3 + h )^2 = ( 3 + h ) ( 3 + h ) = 9 + 3h + 3h + h^2 = 9 + 6h + h^2 . I think it’s called factorising ? 🤯
what is the of the slope tangent line at the given:
y=1׳; at (2,-7)
i need help po what is the answer related architect salamat sa makakasagot
Thank you so much!!!
Where does the 6h come from 😭
Thank you Kind sir
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this is slow jsut find the derivative of x^2 + 1 then plug in 3 and u get 6 u can do it in 5 secs instead of wasting time
so helpful!!
thank u!
Nicely explained
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Thank youuuuuu
so neat!
love u man love u
It's been a while since I've done trig, but most likely yes.
thank you so much
Yeah, show them the hardwar.
Dr Sylvanus P.Thompson wrote on the prologue of his book:
``Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks.
Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics - and they are mostly clever fools - seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.
Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.''
HOT 10/10
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what is h
you should of used the shortcut the derivative of x^2+1 when x=3 then you get 2x then plug in 2(3)=6 much easier
yes, but this is a proof why that power rule works. You got to understand where the equation youre talking about comes from
Brady Bower spoken like a true Math instructor-ha
You saved me from failing Physics
LOL :dddddd 2:11 ROFL OMGG I LAUGHED SO MUCH
same haha
thanks
@eyelykeicecream
and me
its very easy
lol exponent doesnt look like it wants to be there
agree
I feel dumb this is so easy, yet i had trouble ;p
I didn't learn to do it like this :/
Cmmon man u dn't need to waste 6 mins to get that derivative u can ezly calculate the slope jst like this
f'(x)=2 (3)=6 so m=6
no shit dumb ass lol
Thank you so much. Calculus is kicking my white booty!
Way more complicated than it needs to be.
Considering this is the first step in learning derivatives, I think it was well produced. People need to visualize a derivative before they move on to the rules.
wtf is a derivative
Be my teacher.
So why aren't you my teacher ..?