Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The reciprocal of a derivative

  1. Oct 20, 2013 #1
    if dX/dY is the rate of change of X with respect to Y
    say that dX/dY = 3
    now would it be correct if i say that the rate of change of Y with respect to X = 1/3 = dY/dX ?
     
  2. jcsd
  3. Oct 20, 2013 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Yes, it is. (but there are many pitfalls in more general situations!)

    In YOUR case, suppose you are at point (x_0,y_0), where y_0=Y(x_0), and where dY/dX=3.

    That means that in a neigbourhood of (x_0,y_0), Y(x) can be approximated by:
    [tex]Y\approx{y}_{0}+\frac{dY}{dx}|_{x=x_{0}}(x-x_{0})[/tex]
    That is, you function looks like the straight line:
    [tex]y=y_{0}+3(x-x_{0})[/tex]
    Locally, you can invert this relation, solving x in terms of "y", and we may write:
    [tex]x=x_{0}+\frac{1}{3}(y-y_{0})[/tex]

    But, this is "of course", the same as saying, roughly, that dX/dY=1/(dY/dX)=1/3
     
    Last edited: Oct 20, 2013
  4. Oct 20, 2013 #3
    okay i understand but i have two questions
    what does the underscore you used at the beginning mean ?
    in (x_0 ) for instance
    and second , in a linear equation , we describe the slope as the coefficient of (y-y0) Or (x-x0) ?
    or is it such that the rate of change of y with respect to X is the co-efficient of ( x - xnaught ) and the rate of change of X with respect to y in another equation is the co-efficient of (y-y0) ?
    also does this only apply to linear equations ?
     
  5. Oct 20, 2013 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    I use (x_0, y_0) to denote a specific point VALUE, to distinguish from the VARIABLES (x,y)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: The reciprocal of a derivative
  1. Reciprocal Sum (Replies: 11)

  2. Reciprocal functions ? (Replies: 18)

Loading...