### The Essence of Calculus

In this video, we see how unraveling the nuances of a simple geometry question can lead to the essence of calculus.

In this video, we see how unraveling the nuances of a simple geometry question can lead to the essence of calculus.

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

What is an "instantaneous rate of change" when change happens across time? Is it the paradox of the derivative? Here is a beautiful explanation.

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

After introducing the derivative in the last lesson, the next step is to learn how to compute the derivative formulas through geometry.

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

Our goal now is to understand how to take derivatives of more complicated combinations by visualizing the chain rule and product rule.

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

What is Euler's number e? Why are exponentials proportional to their derivatives? We will see why e^x is arguably the most important exponential.

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

Calculus students find it particularly weird to see implicit differentiation for the first time when they are learning calculus.

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

In this lesson, you will understand what it means for one value to approach another, the epsilon-delta definition, and why L'Hôpital's rule works.

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

What is the second derivative? Third derivative? What do you think about these? This lecture is a quick primer on higher order derivatives.

- 3Blue1Brown ,
- Calculus ,
- Mathematics ,

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