*This is an AI generated summary. There may be inaccuracies.*

Summarize another video · Purchase summarize.tech Premium

Differential calculus is a mathematical tool used to calculate the derivative of a function. It was first developed by Isaac Newton in the 17th century, and today it is used to solve a variety of problems in physics and mathematics. The three main rules of differential calculus are the rule of the chain, the sum rule, and the product rule. These rules together form the grammar of differential calculus, and the value of differential calculus can be seen in its many applications, such as calculating the speed of a vehicle traveling in a straight line.

**00:00:00**The differential calculus is a powerful mathematical tool for analyzing change in things. Its foundation is some simple rules for calculating derivatives around 600 years before Christ. Someone discovered that to obtain pleasing harmony, a string instrument's length had to be in relation to simple numbers such as 1 to 2, 2 to 3, etc. That was called the Pythagorean harmony and was an important discovery because it was the first time mathematics and the physical world were related. Unfortunately, that relationship was forgotten and had to be rediscovered slowly and with great difficulty a few centuries later. Galileo was the first to understand it. He wrote: "Después de galileo la física necesitaba un lenguaje más avanzado aproximadamente 25 años después de su muerte se descubriría por fin ese famoso lenguaje y comenzaría a utilizarse a partir de entonces se llamaría cálculo diferencial el cálculo diferencial es muy potente y como en cualquier lenguaje su poder**00:05:00**The derivate is a tool used in cinematics, just as the wheel is for travel. It is a simple tool, but very effective for obtaining a complete perspective on what is a derivate, and there is nothing better than a little exercise to get started. The derivate is not limited to horizontal or vertical motion only; it is the rate of change of any function at any given point. As was explained when discussing the law of gravity, velocity is the derivative of distance, but it is also something more. A derivate can represent the rate of change of any thing, for example, the density of population of dolphins in relation to the decrease in temperature of water or the rate of change of volume of a sphere relative to its area, or the rate of change of price of a pizza with respect to its size. The concept of the derivate is everywhere, but the process of the derivative differential calculus requires a practical approach in order to establish the concept firmly in final terms. Without the rules of differentiation, the concept of the derivate would be a mountain to climb. However, over time, some definitions collected by the path are included herein, so that it may be too late to return to them. Before it is too late, consider the inclination of**00:10:00**This video explains how to calculate the differential of a slope, using an example of a cyclist riding down a hill. The differential is the slope's change in altitude divided by the change in distance. If the slope is constant, then the differential is just the slope itself. If the slope is the same at two points, but the distance between them changes, the differential is the slope multiplied by the change in distance. If the slope changes with both altitude and distance, the differential is just the slope multiplied by the change in altitude. If the slope and distance are constant, but the altitude changes, the differential is the slope multiplied by the change in distance divided by the change in altitude. If the slope and distance are constant, but the altitude changes, the differential is the slope multiplied by the change in distance divided by the change in altitude multiplied by the change in distance. If the slope and distance are constant, but the altitude changes, the differential is the slope multiplied by the change in distance divided by the change in altitude. If the slope and distance are constant, but the altitude changes, the differential is the slope multiplied by the change in distance divided by the change in altitude multiplied by the change in distance divided by the change in distance.**00:15:00**The video explains the differential calculus, a mathematical tool used to calculate the derivative of a function. The calculus is used to calculate the rate of change of a function's position over time, and is used, for example, in carpentry and engineering. One of the main rules of differentiation is the rule of sum, which states that a surface has changed its color over time by summing up the derivative of its height and width over time. The differential calculus also allows for the calculation of derivatives of product and quotient functions.**00:20:00**This video discusses the history of differential calculus, which was first developed by Isaac Newton in the 17th century. Today, differential calculus is used to solve a variety of problems in physics and mathematics. The three main rules of differential calculus are the rule of the chain, the sum rule, and the product rule. These rules together form the grammar of differential calculus, and the value of differential calculus can be seen in its many applications, such as calculating the speed of a vehicle traveling in a straight line. Albert Einstein's theory of relativity is also based on differential calculus.

Copyright © 2024 Summarize, LLC. All rights reserved. · Terms of Service · Privacy Policy · As an Amazon Associate, summarize.tech earns from qualifying purchases.