Search results
- Dictionarydifferentiation/ˌdɪfərɛnʃɪˈeɪʃn/
noun
- 1. the action or process of differentiating or distinguishing between two or more things or people: "packaging can be a source of product differentiation"
Powered by Oxford Dictionaries
See how we define the derivative using limits, and learn to find derivatives quickly with the very useful power, product, and quotient rules. The derivative of a function describes the function's instantaneous rate of change at a certain point - it gives us the slope of the line tangent to the function's graph at that point.
- Differentiate Rational Functions
Differentiate Rational Functions - Differentiation:...
- The Product Rule
The Product Rule - Differentiation: definition and basic...
- Derivative as a Limit
Derivative as a Limit - Differentiation: definition and...
- Differentiate Quotients
Differentiate Quotients - Differentiation: definition and...
- Tangents of Polynomials
The derivative is the rate of change so dy/dx is an...
- Quotient Rule With Tables
Quotient Rule With Tables - Differentiation: definition and...
- Estimate Derivatives
Estimate Derivatives - Differentiation: definition and basic...
- Product Rule With Tables
Product Rule With Tables - Differentiation: definition and...
- Differentiate Rational Functions
Learn the various meanings and uses of the word differentiation, from grammar and biology to geology and psychology. See examples, synonyms, etymology, and related phrases of differentiation.
Jun 21, 2024 · Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. Differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.
- The Editors of Encyclopaedia Britannica
- What Is Differentiation in Maths
- Differentiation Formulas
- Differentiation Rules
- Real-Life Applications of Differentiation
- Solved Examples
- Video Lesson on Class 12 Important Calculus Questions
- GeneratedCaptionsTabForHeroSec
In Mathematics, Differentiation can be defined as a derivative of a function with respect to an independent variable. Differentiation, in calculus, can be applied to measure the function per unit change in the independent variable. Let y = f(x) be a function of x. Then, the rate of change of “y” per unit change in “x” is given by: dy / dx If the fu...
The important Differentiation formulasare given below in the table. Here, let us consider f(x) as a function and f'(x) is the derivative of the function. Also, see:
The basic differentiation rules that need to be followed are as follows: 1. Sum and Difference Rule 2. Product Rule 3. Quotient Rule 4. Chain Rule Let us discuss all these rules here.
With the help of differentiation, we are able to find the rate of change of one quantity with respect to another. Some of the examples are: 1. Acceleration: Rate of change of velocity with respect to time 2. To calculate the highest and lowest point of the curve in a graph or to know its turning point, the derivative function is used 3. To find tan...
Q.1: Differentiate f(x) = 6x3 – 9x + 4 with respect to x. Solution: Given: f(x) = 6x3 – 9x + 4 On differentiating both the sides w.r.t x, we get; f'(x) = (3)(6)x2– 9 f'(x) = 18x2– 9 This is the final answer. Q.2: Differentiate y = x(3x2– 9) Solution: Given, y = x(3x2– 9) y = 3x3– 9x On differentiating both the sides we get, dy/dx = 9x2– 9 This is t...
Practice Problems
1. Find the derivative of the function f(x) = 3 sin x + cos x – tan x. 2. Perform the differentiation for the following functions: (i) f(x) = x3 sin 2x (ii) g(x) = 4xe2x− 9x 3. Find the derivative of the function f(x) = x/(x – 2) (i) Using the limit definition of differentiation (ii) Using the quotient rule To know more about Differentiation and any Maths related topics, please visit us at BYJU’S.
Learn how to find the derivative of a function, also known as differentiation, in calculus. Explore the formulas, rules, applications and examples of differentiation with Byju's Maths.
Learn how to find the slope or rate of change of a function at a point using the derivative formula and examples. The derivative is the limit of the difference quotient as the difference shrinks towards zero.
Learn the meaning, formula, and techniques of differentiation in calculus. Differentiation is the process of finding the rate of change of a function with respect to another quantity.
Definition: Derivative. Let \(f(x)\) be a function defined in an open interval containing \(a\). The derivative of the function \(f(x)\) at \(a\), denoted by \(f′(a)\), is defined by \[f′(a)=\lim_{x→a}\frac{f(x)−f(a)}{x−a} \label{der1} \] provided this limit exists. Alternatively, we may also define the derivative of \(f(x)\) at \(a\) as
