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The partial derivative only acts on one the variables on the equations and treats the others as constant.
Ordinary Diff -> One variable Partial Diff -> More than one variable
Certainly. It uses the same symbol as the full integral, but you still treat the other independent variables as constants.
A functional relation can have two or more independent variables. In order to analyse the behaviour of the dependent variable, it is necessary to calculate how the dependent varies according to either (or both) of the two independent variables. This variation is obtained by partial differentiation.
z=pq