NCERT CLASS 11 || MATHS || Derivatives अवकलज || part 4 || by Hit8OM

#The​​ derivative is a fundamental concept in calculus that represents the rate at which a function changes as its input changes. It measures the sensitivity of the output of a function to small changes in the input. Mathematically, the derivative of a function at a point is the limit of the average rate of change of the function as the interval around shrinks to zero. This is often written as:
f'(x) = \lim_{\Delta x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x}
The derivative of a function can provide various useful insights:
1. Slope of the Tangent Line: The derivative at a point gives the slope of the tangent line to the curve of the function at that point.
2. Rate of Change: It describes how a quantity changes in response to changes in another related quantity, such as velocity (the rate of change of position with respect to time).
3. Optimization: Derivatives are used to find local maxima and minima of functions, which is important in fields like economics, physics, and engineering.
In practical terms, derivatives are used to understand how things change over time or space, and they are critical for modeling and solving problems in science, engineering, and economics.
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