Using limit definition of multivariable derivative

[jamiemmt]

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!

[mrandersdk]

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.

[jamiemmt]

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.