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what is physical significance of partial differentiation?
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To solve the Maxwell's equations, for example...
Geometrically speaking, ∂f∂x may be interpreted as the slope of the tangent line to a surface moving in the x-direction, and ∂f∂y may be interpreted as the slope of the tangent line to a surface moving in the y-direction. A picture is worth a thousand words. In the attached picture, we fix a point P. If we decide to move parallel to the x-axis away from P, the line we walk along has slope equally the partial derivative of f with respect to x at the point P.
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