4 Maths -- Applications of Derivatives

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Differentials

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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

dy=f'(x)\,dx,

where $f'(x)$ is the derivative of f 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

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

df(x)=f'(x)\,dx.

Tangents and Normal:

Equation of Tangent and Normal:

The angle of intersection of two curves:

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