Rules of Derivatives
There are certain rules to be followed while finding the derivatives of functions. Let’s learn from them
Power Rule of Derivative
Following is the Power Rule of Derivatives:
- If f(x) = xn then d(f(x))/dx = dxn/dx = nxn-1
Sum and Difference Rule of Derivative
If two functions are expressed as sum or difference then its derivative is equal to the sum and difference of derivatives of individual function. Let’s say two functions u and v are expressed as u ± v then
d(u ± v )/dx = du/dx ± dv/dx
Constant Multiple Rule of Derivative
If a constant ‘c’ is multiplied to a function f(x) expressed as c.f(x) then the derivative of c.f(x) is given as
d(c.f(x))/dx = c.f'(x)
Product Rule of Derivative
If two functions u and v are given in product form i.e. u.v then its derivative is given as
d(u.v)/dx = u.dv/dx + v.du/dx
Quotient Rule of Derivative
If two functions are given as quotient form i.e. u/v then its derivative is given as
d(u/v)/dx = (v.du/dx – u.dv/dx)v2
Derivatives | First and Second Order Derivatives, Formulas and Examples
Derivatives: In mathematics, a Derivative represents the rate at which a function changes as its input changes. It measures how a function’s output value moves as its input value nudges a little bit. This concept is a fundamental piece of calculus. It is used extensively across science, engineering, economics, and more to analyze changes.
Table of Content
- What are Derivatives?
- Derivatives Meaning
- Derivative by First Principle
- Types of Derivatives
- First Order Derivative
- Second Order Derivative
- nth Order Derivative
- Derivatives Formula
- Rules of Derivatives
- Derivative of Composite Function
- Chain Rule of Derivatives
- Derivative of Implicit Function
- Parametric Derivatives
- Higher Order Derivatives
- Partial Derivative
- Logarithmic Differentiation
- Applications of Derivatives
- Derivatives Examples
- Sample Problems on Derivatives
- Practice Problems on Derivatives
A derivative is a calculus tool that measures the sensitivity of a function’s output to its input. It is also known as the instantaneous rate of change of a function at a given position.
The derivative of a function with just one variable is the slope of the line that is tangent to the function’s graph for a given input value. In terms of geometry, the derivative of a function can be defined as the slope of its graph.
In this article we have covered Meaning of Derivatives along with types of derivatives, examples, formulas, applications and many more.