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Very little. An algorithm is a method that has been expressed in a detailed, unambiguous form.
They Are both ways to express partial #'s
Suppose, Z is a function of X and Y. In case of Partial Differentiation of Z with respect to X, all other variables, except X are treated as constants. But, total derivative pf z is given by, dz=(partial derivative of z w.r.t x)dx + (partial derivative of z w.r.t y)dy