deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 7980317..a573b0d 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\begin{align*}  (ln|f(x,y)|)_x &= [ln(\sqrt{u^{2}+v^{2}})]_x\\  &= \frac{1}{2}[ln(u^{2}+v^{2})]_x  &=\frac{2uu_x+2vv_x}{2(u^{2}+v^{2}}  \end{align*}  \end{proof}