# Partial derivative using the definition

1. Oct 26, 2011

### U.Renko

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

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

3. The attempt at a solution

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

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

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.