Explanation of a Derivative in Calculus : Calculus Explained

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Before you can work with derivatives in calculus you're going to need to know precisely what one is. Get an explanation of a derivative in calculus with help from an experienced math tutor in this free video clip.

Expert: Ryan Malloy
Filmmaker: Patrick Russell

Series Description: Calculus is a more advanced mathematical topic than others, so feeling a little overwhelmed from time to time is only natural. Get an explanation for a wide variety of different calculus terms and situations with help from an experienced math tutor in this free video series.

[momo_drum]

I now understand how guys must feel watching mathbff.
Easier and harder to focus when the instructor is gorgeous.

[mr_underscore]

When I search "simple explanation", I expect an explanation an average human brain could understand not something which is full of technical terms and definitions, because my book already has that crap.

[darthglowball]

I don't get it when you try using the formula: (f(a+h)-f(a))/h to calculate the derivative. If h goes to zero, then the formula becomes: (f(a+0)-f(a))/0 = (f(a)-f(a)/0) = 0/0 = an undefined This does not look like a valid slope... Should I take a value for h that is really small, but not zero?

[wanderingpalace]

Thx dude
My teacher was teaching in a way that everyone in my class dont understand this
But now i can
Ur explanation is easy to follow
Thx bro <3

[TheAronWelsh]

My apologies if this question seems very basic or perhaps doesn't even make sense. If the derivative of that point will give us the slope of that line, that must mean that line is passing that point at a very specific angle. So my question is if the line was to pass the point at a different angle would the derivative be different? Or is that the only line (therefore only slope) that would correlate with the derivative of that particular point?

[katmor]

you wrote in both lim (h-->0), i.e. h approaching to cero. The thing that is not clear for me is, if both are approaching to cero, why the yellow one (the above one) goes rightwards and the pink one (the below one) goes leftwards. Shouldn´t be the first one (the yellow one) a positive one and the second one a negative one? I mean, if both are approaching to cero, why do they go in opposite directions? Would be glad, if I could get an answer. Thank you!

[awayahmed]

hi can you answer this question: 1. Leonardo will again step in his Bugatti Veyron. He drives back from Pisa to Milan with an average of 380 km / h. He here about 3 minutes. On the way back, he again finds himself in a traffic jam. The traffic jam is 10 km long and here he is doing about 1.5 hours. Following is still 60 km slow traffic of 40 km / h. After Leonardo're gone can continue normally. In total, its average speed is measured on the way back and 114 km / h. What is his average speed on the way back to the piece without queues or slow traffic?

[Metaconcept]

Thanks for throwing the terms "instantaneous rate of change" and "velocity" into it Your vid made things a lot clearer!

[conantheseptuagenarian]

instantaneous rate of change is a contradiction in terms.

[nolimit]

THIS ACTUALLY MADE SENSE TO ME OVER 3 BLUES ONE BROWN VIDEO! Thank yoU!

[brndyfranklin]

Very well explained. I myself am totally inept in mathematics and could conceptualize what was happening.

[AdamT]

isnt there an easier way, where you multiply the base with its exponent relative to x and then subtract 1 to the exponent of the x ...? or is that what he meant in the second equation?

ex.
f^1(x) = 3x^3+2x^2-4x+2
f^1(x) =
f^1(x) = 6x^2+4x-4

[mattyjmar]

Great video! Thanks for the great video with a practical explanation.

[konsueloramirez]

I want him to be my permanent math tutor :)

[Aerospaceman]

In the Navy, the tangent line may represent the closest point of approach of a vessel, or it could represent an inbound or outbound course or speed. Its instantaneous, but no one ever tells you about the secant line connecting the two tangent points. This now makes perfect sense. Nice video, Thanks.

[TheChaney]

This kind of math usually turns me into a shit-eating baby, but I actually understood it this time around. Yay.

[MsBijay]

one thing noone explains...why draw a tangent line at the first place? i don't need/want to watch more to know definitions (what part) that every prof says but the reasoning behind doing something (why part)..hope someone here can help me

[RutabagasINSandCastleS]

It's official I'm incompetent hahahahaha

[sidmajumder]

Why is the limit h--0? I can't understand

[VndNvwYvvSvv]

Good video. Technically, "instantaneous rate of change" is an oxymoron, impossible, and not the correct way to represent it, but it is apparently one of the easiest ways to understand the concept.