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Partial derivative using the definition

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data

    So I'm supposed to find the partial derivatives and calculate them at point (0,2) using the definition


    2. Relevant equations

    [itex] f(x,y) = x^2y\sin(1/x) [/itex] IF x ≠ 0
    [itex] f(x,y) = 0 [/itex] IF x = 0



    3. The attempt at a solution

    [itex]\frac{lim_{\Delta_x\rightarrow0} = (x + \Delta_x)^2y\sin(1/x+\Delta_x) - x^2y\sin(1/x)}{\Delta_x}[/itex]



    the thing is, I'm not very sure how to solve
    [itex] \lim_{\Delta_x\rightarrow0} \sin(1/x+\Delta_x) [/itex]

    and if I just consider it the same as sin(1/x)
    things get messed up

    also this is my first time using LaTex.
    Hope I did fine.
     
  2. jcsd
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