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Thread: Derivative function

  1. #1 Derivative function 
    Member pienapple27's Avatar
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    It said on wikipedia (Derivative - Wikipedia, the free encyclopedia) that in a funcion of the type y=mx+b the slope, m, is given by (change in y)/(change in x). What is this change and how do I measure/calculate it?
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  2. #2  
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    You take two points on the line (x1,y1) and (x2,y2) and then you calculate (y2-y1)/(x2-x1).
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  3. #3  
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    Ok! Here's what I understand (from the wikipedia page): The simplest case, apart from the trivial case of a constant function, is when y is a linear function of x, meaning that the graph of y divided by x is a line. In this case, y = f(x) = m x + b, for real numbers m and b, and the slope m is given by change in y divided by change in x. It follows that Δy = m Δx. This gives an exact value for the slope of a line.
    This is what I don't understand very well (from the wikipedia page): If the function f is not linear (i.e. its graph is not a line), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.
    Can you explain this to me?
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  4. #4  
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    If you have a curve rather than a straight line you have to consider just a really really tiny section of the line to get the exact slope. In fact to get it precise the length of the segment has to tend to zero. That is differentiation.
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  5. #5  
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    See how you get on with this:
    Introduction to Derivatives
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  6. #6  
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    Now I have to go, but I'll read that later. I just want to say thanks for answering and explaining my questions!
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  7. #7  
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    YAY! I've learned how to differenciate (the basics at least)! Thank you!
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  8. #8  
    KJW
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    Quote Originally Posted by pienapple27 View Post
    YAY! I've learned how to differenciate (the basics at least)! Thank you!
    To properly understand this, you need to understand the notion of the limit.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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  9. #9  
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    that's why I can properly understand this but thank you anyway
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