The general form of Leibniz's Integral Rule with variable limits can be derived as a consequence of the basic form of Leibniz's Integral Rule, the Multivariable Chain Rule, and the First Fundamental Theorem of Calculus. Suppose formula_93 is defined in a rectangle in the formula_94 plane, for formula_95 and formula_96. Also, assume formula_93 and the partial derivative formula_98 are both continuous functions on this rectangle. Suppose formula_99 are differentiable real valued functions defined on formula_100, with values in formula_101 (i.e. for every formula_102). Now, set