Differentials and True Change

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If z=x^2+y^2, find both dz and delta z, as well as the error that one commits if dz is used instead of delta z.

So far I have dz=2xdx+2ydz.

However, I am not sure how to calculate delta z. Also not sure what the error would be.

Any help would be great, thanks.

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Using function notation, Let $f(x,y)=z=x^2+y^2$.
Then $\Delta z=f(x+\Delta x, y+\Delta y)-f(x,y)$.

To compare $dz$ and $\Delta z$, use $dx=\Delta x$ and $dy=\Delta y$.