Calculus का रहस्य | Differentiation the invention which changed the mathematics

What is calculus ?
The word Calculus comes from Latin meaning "small stone",
Because it is like understanding something by looking at small pieces.
Differential Calculus cuts something into small pieces to find how it changes.
Integral Calculus joins (integrates) the small pieces together to find how much there is. Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions .Differentiation allows us to find rates of change. For example, it allows us to find the rate of change of velocity with respect to time (which is acceleration). It also allows us to find the rate of change of x with respect to y, which on a graph of y against x is the gradient of the curve. There are a number of simple rules which can be used to allow us to differentiate many functions easily.
If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x" .
Differentiating x to the power of something
1) If y = xn, dy/dx = nxn-1
2) If y = kxn, dy/dx = nkxn-1(where k is a constant- in other words a number)
Therefore to differentiate x to the power of something you bring the power down to in front of the x, and then reduce the power by one.
In Isaac Newton's day, one of the biggest problems was poor navigation at sea Shipwrecks occured because the ship was not where the captain thought it should be. There was not a good enough understanding of how the Earth, stars and planets moved with respect to each other.
Calculus (differentiation and integration) was developed to improve this understanding.
Differentiation and integration can help us solve many types of real-world problems.
We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, limits, 0 and infinity, infinitesimal, division by 0 etc.).
Derivatives are met in many engineering and science problems, especially when modelling the behavior of moving objects and with history of calculus.
Our discussion begins with some general applications which we can then apply to specific problems.
Calculus का रहस्य | Differentiation the invention which changed the mathematics
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