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Differentials

Differentials:

In calculus, the differential represents the principal part of the change in a function y = f(x) with respect to changes in the independent variable. The differential dy is defined by

where  is the derivative of  with respect to x, and dx is an additional real variable (so that dy is a function of x and dx). The notation is such that the equation

holds, where the derivative is represented in the Leibniz notation dy/dx, and this is consistent with regarding the derivative as the quotient of the differentials. One also writes



Tangents and Normal:



Equation of Tangent and Normal:


The angle of intersection of two curves: