# 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

${\displaystyle dy=f'(x)\,dx,}$

where ${\displaystyle f'(x)}$ 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

${\displaystyle dy={\frac {dy}{dx}}\,dx}$

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

${\displaystyle df(x)=f'(x)\,dx.}$

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Tangents and Normal:

Equation of Tangent and Normal:

﻿The angle of intersection of two curves: