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B Why did they change the sign to be negative?

  1. May 25, 2016 #1

    JR Sauerland

    User Avatar
    Gold Member

    http://imgur.com/BNQPAQa

    I'm missing something. Why does x+1/x suddenly become x-1/x2? I get that they moved the x to the top, subtracted the -1-1, but does that exclusively set the fraction negative all on its own ? I've computed it by hand. 1-2 comes out to be 1... So why is it negative... ?
     
  2. jcsd
  3. May 25, 2016 #2

    jedishrfu

    Staff: Mentor

    Starting with ##y=1/x## then you can write it as ##y=x^{-1}## and then using the rule ##dy/dx = d/dx(x^n) = nx^{n-1}## you get ##dy/dx=(-1)x^{-1-1} = -x^{-2} = -1/x^2##

    In the bottom line of the picture, they are evaluating ##d/dx(x + 1/x)## as an example which is ##d/dx(x) + d/dx(1/x) = 1 -1/x^2##
     
  4. May 25, 2016 #3

    Mark44

    Staff: Mentor

    You're missing two things:
    1) It isn't "x - 1/x2" It's ##1 - \frac 1 {x^2}##. At the very least,use ^ to indicate an exponent, as in 1 - 1/x^2.
    2) They are differentiating x + 1/x to get It's ##1 - \frac 1 {x^2}##, but they wrote what they're doing very poorly, IMO.
    ##\frac d {dx}(x + \frac 1 x) = \frac d {dx} x + \frac d {dx} x^{-1} = 1 + (-1)x^{-2} = 1 - \frac 1 {x^2}##

     
  5. May 27, 2016 #4
    The image is extremely awkwardly worded. You should not feel bad for not getting it. It is just a terrible way of teaching this topic.

    What happened is that it recognized that ##1/x## can be re-written as x^-1, and then you apply the power rule of differentiation: derivative of ##x^n## is nx^(n-1).

    In our case, n = -1, so nx^(n-1) is -1 * x ^ (-1 -1) = - x^-2 = 1/x^2
     
  6. May 27, 2016 #5

    Mark44

    Staff: Mentor

    At the end you lost the sign. It should be ##\frac {-1} {x^2}##
     
  7. May 27, 2016 #6
    Yes I did. The equation maker here is very bad with exponents, got me all messed up.
     
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