The derivative in calculus applies to curvature - Newton was trying to explain variations in planetary orbits, along with Kepler, after all .. Newton's law of gravity is an inverse square law relating mass to radius of an orbit - Note: it actually gets more complicated...

John Gabriel (barely and only occasionally) manages to work out that the derivative of a

**straight line **y = f(x) = Ax + b is the constant A for any point on the line.

f'(x) = A (independent of x, and therefore dx)

Infinitesimal calculus solves problems relating to non-linear functions (i.e., curvature).. which he rejects (along with

, e, and complex numbers as having no relevance in his world (which is primarily good for counting change at McDonald's)...

His ignorance comes from trying to teach calculus to himself without understanding Analytic Geometry (which is its foundation). John Gabriel desperately needs to take (and pass) pre-calculus courses at a junior college somewhere .... As of now, I don't think he can post a GPA from anywhere.

Analytic Geometry
(The ticks on the axes appear as integers, but the spaces between them are filled by real numbers, at least some of which come from projecting trigonometric functions onto the axes)..

"In

geometry, the

**tangent line** (or simply

**tangent**) to a plane

curve at a given

point is the

straight line that "just touches" the curve at that point. Informally, it is a line through a pair of

infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve

*y* =

*f*(

*x*) at a point

*x* =

*c* on the curve if the line passes through the point (

*c*,

*f*(

*c*)) on the curve and has slope

*f*'(

*c*) where

*f*' is the

derivative of

*f*. A similar definition applies to

space curves and curves in

*n*-dimensional

Euclidean space."

For more insight, follow the links...

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