[Blindmath] D Y verses Delta Y

[Sean Tikkun]

The difference is one of magnitude.  delta y / delta x is a ratio.  It has concrete values for the numerator and denominator.   dy / dx by contrast is the derivative of the function y with regard to the variable x.  dy / dx is a function, and as such will not have a single value.  It is a relationship.  understanding this principle and being able to execute it is critical before moving on to multivariable calculus where you can take the derivative of a function with regard to different variables.

Sean Tikkun
Instructor
Northern Illinois University

srtikkun at niu.com




On Apr 5, 2013, at 3:07 AM, "Fernández del Campo Sánchez, Jose Enrique" <EFCS at once.es> wrote:

> "Delta" or "increment" are magnitudes, quantities: when you increment q quantity delta x, on obtains an increment delta y of the function y=f(x).
> 
> But "differential" d x and d y are concepts relatif to derivative.
> 
> It is very simple if you see then raphically, calling to the tangent of the courbe. And in multivariable functions, they are not comparable.
> 
> 
> 
> Saludos
> 
>      José Enrique
> 
> 
> 
> -----Mensaje original-----
> De: Blindmath [mailto:blindmath-bounces at nfbnet.org] En nombre de GianniP46
> Enviado el: viernes, 05 de abril de 2013 6:13
> Para: BlindMathList
> Asunto: [Blindmath] D Y verses Delta Y
> 
> Hi all,
> I am brushing up on some Calculus.  I find myself confused between the difference d y and delta y and d x and delta x.  It seams that d x and delta x are usually the same, but there is a difference between d y and delta y.
> For example, if you have a function Y = X squared, and you want to find d y and delta y at x = 2 and d x =1, Then D Y = 2X DX which = 2 times2 times 1 which =4 Delta y = f of x plus delta x minus f of x which = (x + delta x) squared minus x squared which = (2+1) squared minus 2 squared which = 9  minus 4 = 5 so d x = 4 and d y = 5.
> 
> I understand that d y is the y component or the rise of the slope of the tangent line at x = 2 of x squared, but what does a delta y value of 5 mean for this function?
> 
> The book I am looking at makes it seam that d y has to do with the y component of the tangent line and delta y has to do with the y component of the curve.  This is not making sense to me for some reason.  Can someone explain?  Feeling very dumb and frustrated right now. lol
> 
> 
> Gian Carlo Pedulla
> GianniP46 at earthlink.net
> 
> LETS! GO! METS!
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