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Math Help - Can somebody tell me what the dy/dx is about?

  1. #1
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    Can somebody tell me what the dy/dx is about?

    I have tried and tried to read the pages in my math book about it, but I just can't seem to understand what is meant by the dy/dx?

    So far, I have seen this in implicit differentiation, integration by parts and integration by substitution.

    It seems like dy/dx is differentiation? But why do you use it in integration as well? And why do you sometimes differentiate with y and other times with x and so on.

    I don't get this at all. I have tried to read it in my school book but they don't even tell you what it's for. They just say that when you need to do one of the three methods, you just multiply by dy/dx and etc. It makes no sense to me. every time I see the dy/dx I just get confused and i have no idea what's going on....
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  2. #2
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    Quote Originally Posted by No Logic Sense View Post
    I have tried and tried to read the pages in my math book about it, but I just can't seem to understand what is meant by the dy/dx?

    So far, I have seen this in implicit differentiation, integration by parts and integration by substitution.

    It seems like dy/dx is differentiation? But why do you use it in integration as well? And why do you sometimes differentiate with y and other times with x and so on.

    I don't get this at all. I have tried to read it in my school book but they don't even tell you what it's for. They just say that when you need to do one of the three methods, you just multiply by dy/dx and etc. It makes no sense to me. every time I see the dy/dx I just get confused and i have no idea what's going on....
    Your question is not very specific so hard to answer but hopeful I can make a useful comment, even if it doesn't answer everything.

    When you think of slope you measure rise and divide by run. So if you have two points (x_1,y_1) and (x_2,y_2), then the average slope is

    Slope = \frac{y_2 - y_1}{x_2 - x_1}

    So the difference we label with the Greek symbol delta \delta

    Slope = \frac{\delta y}{\delta x}

    Now consider the points becoming closer and closer together. The deltas which are finite are replaced with infinitessimals dy and dx and then you have the continuous slope is

    Slope = \frac{dy}{dx}

    So in some sense you can think of these things as discrete differences in the limit of them approaching a continous change.

    Hope this helps
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  3. #3
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    So it's like saying:

    lim_dx ---> 0 ???

    but I think I remember reading somewhere that delta isn't the same as "d"?
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  4. #4
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    Using the letter "d" is for when referring to a derivative. It's not as hard as it seems. I remember not getting it at first either. dy/dx means that there is a function, y, written in terms of variable x. That's what the dy tells us. The dx on bottom tells us that the derivative of function y has been calculated with respect to the variable x. You could find the derivative in respect to other variables, say "t" which would look like dy/dt. When you see "d/dx" there will be an expression directly following and this notation says to calculate the derivative of this expression with respect to x. dy/dx is not the same as delta(y)/delta(x). The letter "d" indicates an instantaneous change as the result of a limit where the letter delta is an actual change between two given points.

    Summary: dy/dx means the derivative of function y with respect to x. It doesn't mean anything useful standing alone, which is why you see it in equations.
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  5. #5
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    Quote Originally Posted by No Logic Sense View Post
    So it's like saying:

    lim_dx ---> 0 ???

    but I think I remember reading somewhere that delta isn't the same as "d"?
    Yes, formally it is precisely the limit as \delta x \rightarrow 0. So if y(x) is a function of x then the derivative is defined as

    \frac{dy}{dx} = \lim_{\delta x \rightarrow 0} \frac{y(x+\delta x) - y(x)}{\delta x}

    This is what I was attempting to explain in words. So dx is not the same as \delta x but you can think of one in terms of the limiting behaviour of the other.
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