If I have w(x, y, z) and take "dw = (∂w/∂x)dx + (∂w/∂y)dy + (∂w/∂z)dz"; doesn't that accurately describe how w changes as x, y and z change by an infinitesimal? Or does that only work for some special cases?(adsbygoogle = window.adsbygoogle || []).push({});

I feel like if I take the total derivative I am actually describing how the function w changes with respect to an infinitesimal change in a parameter t. Or to one of the variables which all the other variables happen to depend on, not the variables x, y and z. Is that right?

Also, does "dw = (∂w/∂x)dx + (∂w/∂y)dy" mean that if I go one unit in the direction of x and one unit in the direction of y I will have climbed "(∂w/∂x) + (∂w/∂y)" along the direction of w?

Which is kind of like going one for x and one for y along the tangent plane?

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# Motivation to Create the Total Derivative

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