Applications of Derivatives

What is Derivatives?

Derivatives are defined as the ratio of the rate of change of one variable with respect to the other variable i.e., dy/dx shows the change in the variable y with respect to the change in the variable x.

What is the Derivative of a Function?

 The derivative of a function represents the rate of change of the function at any point on the function. It is defined as the slope of the tangent line to the function at that point.

How to Find the Derivative of a Function?

Find derivatives there are various ways that can help such as chain rule, quotient rule, power rule, etc. Other than that for a detail description of the same you can read the article “How to find derivative?”

What are Application of Derivatives?

Application of derivatives in mathematics include Rate Change of Quantities, Increasing and Decreasing Function, Approximation, Maxima and Minima, Tangents and Normal Lines, etc.

What is Difference between First Derivative and Second Derivative of a Function?

The difference between the first and second derivative is simple i.e., when you differentiate the function for the first time, result is called first derivative, and when you again differentiate the first derivative the result is called the second derivative.

What is Difference between Monotonically Increasing and Increasing Function?

The key difference between monotonically increasing and increasing function is that for increasing function for any two input values x₁ and x₂  such that x₁>x₂, increasing function always holds f(x₁)>f(x₂) but for monotonically increasing function for any two input values x₁ and x₂  such that x₁>x₂, monotonically increasing functions holds equality as well i.e., f(x₁) ≥ f(x₂).

How to Find the Equation of Tangent?

Equation of tangent at a point (x, y) for any function y = f(x) is given as follows:

(Y – y) = dy/dx × (X – x)

How to Find the Equation of Normal?

Equation of Normal at a point (x, y) for any function y = f(x) is given as follows:

(Y – y) = -dx/dy × (X – x)

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.