The Derivative in Calculus Defined as a Limit - [1-2]

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In this lesson, you will learn what the mathematical definition of a derivative is in calculus. The derivative is defined to be the slope of the line tangent to a function at a point. In order to do this, we find the slope of a line passing through two far away points, then slowing move these points closer together using the limit process. The derivative is then defined to be the slope of the line tangent to the function at a given point, and is calculated to be the slope of the line through two points, as the limit takes these two points to be infinitely close together.

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[@hemrajue3434]

I think slope definition gives us slope between two discrete points whereas the limit definition of derivative gives us the slope at a point of a continuous curve.

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Very well said!

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[@iancasey1486]

Damn! I think you just nailed it!🎉🎉 1. Slope(of a curve) - A straight line touching two points along a curve! Any two points in between may have a different slope. 2. Limit - The point on the curve and from which a slope can be derived! Wow! Limit definition is one point along the curve WHERE a slope can be derived! So, when the line touches two points along the curve is a slope. A line touching one point is the limit from which a slope can be 'derived'!

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[@kostaskostas2470]

It’s a good video but your argument that teaching limits is ridiculous is unfortunate. Calculus is all about limits. Limit is the revolutionary idea that allows calculus to develop. It is sad and not good to see calculus as differentiation and integration and teach the rules.

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