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The derivative of a function is another function that represents the slope of the function at each of the points in the original function's domain.

For instance, given the function f(x) = x2, the derivative is f'(x) = 2x. This says that the slope of the original function f(x) = x2 is 2x at every x. This is very useful when you want to graph the function, because you only need a few data points, and then you can quickly sketch the shape of the curve when you know the slope.

Later on, you are going to learn about anti-derivatives, and you are going to call them integrals, and you are going to learn the vast power of this thing we call calculus in terms of finding the area under a curve, but let's take it one step at a time.

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How derivatives are helpful to find the behavior of graph of function'?

(1) Derivatives are useful tools for providing information about the behaviour of the graph.(2)Derivatives helps to measure the steepness of the graph.(3)Derivatives gives us information wether the graph is increasing or decreasing.(4) Derivatives Helps us to determine maximum,minimum value,and crital pointsof graph. hope it will help Kalim Raja


Who discovered derivatives in mathematics?

Isaac Newton and Göttfried Leibniz simultaneously and indepently created calculus as we know it and derivatives with it. (Late 17th century)


What are the two derivatives for zephyr?

The two derivatives for "zephyr" are "zephyrous," which describes something that is light or airy, and "zephyrlike," which refers to qualities reminiscent of a gentle breeze. Both derivatives capture the essence of zephyr as a soft, gentle wind often associated with spring.


What are various uses of derivatives?

Derivatives have several key applications across various fields. In finance, they are used for hedging risks and speculating on price movements of assets. In mathematics and physics, derivatives help analyze rates of change and optimize functions, providing insights into motion and other dynamic systems. Additionally, derivatives are essential in engineering for modeling and controlling systems, as well as in economics for understanding marginal costs and benefits.


Who created derivatives in math?

Sir Isaac Newton and Leibniz.