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[tex]dz=\frac{}{}\partial z/\partial x dx+\frac{}{}\partial z/\partial y dy[/tex]

but when i try to integrate it, the right side of the equation is equal to z times the number of dimensions you're dealing with.

[tex]\int dz=\int\frac{}{}\partial z/\partial x dx+\int\frac{}{}\partial z/\partial y dy[/tex]

[tex]z=z+z[/tex]

Is there something unique in total derivatives that im missing that doesn't allow me to integrate like this? or am i making a horrible assumption with integrating partial derivatives in that they are the same as regular derivatives when integrating in respect to the same thing? My high school calculus teacher can't help me because he hasn't done this kind of math since college, which was quite some time ago. This isn't a homework problem (my actual homework is quite boring), just something i ran into on accident while studying ahead in my book that has me confused.