Skip to main content\(\newcommand{\R}{\mathbb{R}}
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A three dimensional plot of a curved surface shown in gray above a set of axes labeled
\(x\text{,}\) \(y\text{,}\) and
\(z\text{.}\) An arrow is shown below the surface on the xy-plane in blue. This arrow is labeled with
\(\langle a ,b \rangle\) and as “change in input” while pointing in the direction of the x and y axes. Line segments from the ends of the blue arrow to the surface are drawn in gray. From the two points where the gray segments intersect the surface, there are two red segments that move parallel to the xy-plane to the z-axis. The distance between where the two red line segments intersect the z-axis is shown with red arrows and labeled as “change in output”.