Total differential of a multivariable function

[Rishabh Narula]

Please refer to the images and my handwritten note(i tried my best handwriting) for the question

 

[FactChecker]

There is a horizontal plane (z constant) through the point P. They are identifying a rectangle in it as PDEF. There is nothing there that one can argue with. It is not "sloped". With that in mind, you should reconsider your thinking.

PS. If you type your statements in, then it is easier for people to comment on specific parts of it.

 

[Rishabh Narula]

Thanks,will do that next time onwards.Is the short proof right,that the different partials multiplied by small changes in different dimensions,when added up give the total small change?

 

[FactChecker]

That is what is defined as the "total differential".