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Say that:

$$z = xy$$

So:

$${\partial z \over \partial x} = y$$

and

$${\partial z \over \partial y} = x$$

If we plot in 3D space the 2D surface corresponding to eq1, than take a point on that surface, the tangent with respect to the x axis is y, and the tangent corresponding to the y axis is x.

Do the total derivatives ($dz \over dx$ and $dz \over dy$) have a similar geometric interpretation?

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    Total derivative is $dz=z_xdx+z_yd_y$.2012-10-26

3 Answers 3