Derivatives Definition
Derivative of a variable y with respect to x is defined as the ratio between the change in y and change in x, depending upon the condition that changes in x should be very small tending towards zero.
dy/dx = lim ∆x⇢0 ∆y / ∆x = lim h⇢0 (f(x + h) – f(x)) / h.
Where,
- ∆x OR h is change in x, and
- ∆y OR f(x + h) – f(x) is change in y.
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Application of Derivatives
Derivatives are a fundamental concept in calculus. They measure how a function changes as its input changes. This makes Derivatives very useful in various fields. For example, derivatives help in understanding motion, growth, and change in physical, economic, and engineering systems. They are used to find rates of change, slopes of curves, and to solve optimization problems. By understanding derivatives, we can predict how things will change and make better decisions based on this information.
Table of Content
- Derivatives Definition
- Application of Derivatives in Math
- Rate Change of Quantities
- Increasing and Decreasing Function
- Approximation
- Monotonicity
- Maxima and Minima
- Tangent and Normal
- Real-Life Applications of Derivatives
- Sample Problems on Applications of Derivatives
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