Applications of Derivatives Class 12 Mathematics Notes has been updated according to the latest syllabus of 2080. It means the notes of applications of derivatives chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of this chapter because we are here to serve you.
Chapter – 13
Applications of Derivatives
In Class 12 Mathematics, the chapter on “Applications of Derivatives” covers a variety of important topics that illustrate how derivatives are used in real-world scenarios and problem-solving.
Rate of Change of Quantities
Derivatives are used to determine the rate at which one quantity changes with respect to another. For example, if $latex y = f(x)$ represents the position of an object at time $latex x$, then $latex f'(x)$ represents the velocity of the object, showing how its position changes over time.
Class 12 Applications of Derivatives Notes PDF
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Differentials
Let $latex y = f(x)$ be a function of $latex x$. Then,
- The differential, $latex dx$, of the independent variable $latex x$, is an arbitrary increment of $latex x$; that is, $latex dx = \Delta x$.
- The differential, $latex dy$, of the dependent variable $latex y$ is $latex dy = f'(x) \cdot dx$ where $latex f'(x)$ is the derivative of $latex f(x)$.
- While the differential $latex dx$ of the independent variable is an increment $latex \Delta x$, the differential $latex dy$ of the dependent variable is not, in general, equal to the corresponding increment $latex \Delta y$.
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