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/sci/ - Science & Math

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3856931 No.3856931 [Reply] [Original]

I'm trying to get a better more intuitive understanding of the difference between "dy" and Delta y. If a derivative is dy/dx, which is the slope of the tangent line to any given point on a function, and dx is simply any change in x, then is "dy" simply the change in the numerator of the slope of the tangent line at any given point on the function, for any given change in x of that point? If that is the case, I'm still not sure I understand what that means, and how it is different from "Delta y", which I understand to be the change in y for any change in x at point x. Would it be correct to say that dy is the change in change in y, and Delta y is just the change in y?

>> No.3856945

delta Y = change in Y

When the change in y approaches 0, it's written as dy.

>> No.3856986

>>3856945

Then why is dx equal to delta x even when it doesn't approach zero?

>> No.3858696

>>3856931
Do you understand differentiation via first principles OP?

If not.. The basic concept is that if we draw a line between two points and use the gradient formula
{ie. m=(y2-y1)/(x2-x1)}.
As these points apprach each other we get more accurate results. When they are in the same spot we divide by zero.
dy/dx is what is written in these situations.
Delta y/ Delta x is what is written when you find the gradient between two DISTANT points (such as where x1=1 and x2=1.0001)
Does this help OP?

>> No.3858703

dx and dy are the limits of delta-x and delta-y, respectively, as dx goes to zero.

>> No.3858710
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3858710

>>3858703
>dx and dy are the limits of delta-x and delta-y, respectively, as dx goes to zero.
>dx is the limit of delta-x as dx goes to zero.
>mfw

>> No.3858761

d-anything is an infinitesimally small change in that variable.

>> No.3858927

dy is instantaneous
Δy is not

>> No.3858938

delta y is finite, dy is infinitesimal.

>> No.3858966

dy is a differential form. Delta y is change in y.

>> No.3859173

in a completely non mathematical language, the tangent line is the limit of secant lines

that's the best way to visualize dy/dx as the limit of delta y