Total Differential of Multivariate Function f(x, y) = x^3y^4 + x^2y^3 + 12

Total Differential of Multivariate Function f(x, y) = x^3y^4 + x^2y^3 + 12

[wookiecookie]

Hello. I hve a doubt in this.. wont we do dx and dy further ? Like do we have to further differentiate the terms wrt dx and dy as in this equation? Or this is the final answer?

[maxpercer]

Is there a proof that df = fx * dx + fy * dy is the total differential? Or is that just the definition?
It does resemble the one variable differential dy = f'(x) dx.

[isobar]

Begs the question : " why are we doing this", any clarification would be greatly appreciated and thanks.

[TPLCreationLoft]

Why isn't the total differential written as a vector consisting of each partial derivative?

[JMRG]

I'm strugling to understand the difference between the symbol d and ∂, since it all looks like partial derivates why we don't use d for everything instead of ∂? If I'm optimizing a function, shall I use ∂ instead of d? since I'm not interested in finding the derivative of other variables rather than just one. E.G. y(x, z, w)= ax + bz +cw

Optimization will tell me that equal partial derivates to each variables as 0, then can I write it like:

∂y/∂x= a
∂y/∂z= b
∂y/∂w=c

Is this good or I have to use d instead?

[milos]

Is this formula related to the implicit differentiation?

[kevenwijaya]

hey my math teacher adds error in the question, so what is the error ? is that the dx, dy or something?