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Using limit definition of multivariable derivative

  1. Feb 4, 2008 #1
    Hi, everyone-

    I have a quick question. When you solve for the derivative (as a linear transformation) using the limit definition of derivative, how does it go?

    For example, let p_k be defined as the projection function from Rn to R, projecting onto kth coordinate of the input value.

    lim _(h->0)=\frac{f(x+h)-f(x)}{h}=lim_(h->0)\frac{|h_k|}{h}=??

    I see that the linear transformation of h is eqal to the numerator in this case (and that p_k is a linear transformation) but I thought that T had to depend upon x, not h...

    Thanks!
     
  2. jcsd
  3. Feb 4, 2008 #2
    what is T, how do you get

    \frac{f(x+h)-f(x)}{h}=\frac{|h_k|}{h}

    and what is your question it is impossible to understand.
     
  4. Feb 4, 2008 #3
    f(x+h)=x_k+h_k
    f(x)=x_k
    so f(x+h)-f(x)=h_k

    so I am looking for T= the linear transformation, or the value of this limit.
     
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