Differentiation From Wikipedia, the free encyclopedia Differentiation may refer to: Science, technology, and mathematics[edit] Biology and medicine[edit] Geology[edit] Social sciences[edit] Other uses in science, technology, and mathematics[edit] In business[edit] See also[edit] Idea: Differentiation In Michael Porter's ground-breaking work on the competition of the firm he argued that there are only two ways for firms to compete: by charging a lower price, or by differentiating their products or services from those of their rivals. This differentiation can take real forms (soluble aspirin as against non-soluble aspirin, for example) or imaginary forms (by advertising that suggests one perfume makes you more attractive to the opposite sex than another). The value of differentiation increases the more that products come to resemble each other. For example, different brands of airline flight or latte vary less and less as time goes by. So it becomes a bigger and bigger challenge to differentiate one from another. Once a clear distinction has been established, however, it can be reaffirmed for years and years. In consumer-goods industries it is common for a large number of differentiated products to be produced by a small number of firms. Further reading More management ideas
Cell Differentiation | Ask A Biologist In order for cells to become whole organisms, they must divide and differentiate. Cells divide all the time. That means that just one cell, a fertilized egg, is able to become the trillions of cells that make up your body, just by dividing. Those trillions of cells are not all the same though. Just a little while after you started out as a fertilized egg, your cells started performing specific tasks, even started to look different because of that. The example of this is your lung cells and your brain cells. Scientists still do not understand perfectly why cells in the same organism decide to differentiate. Scientists thought that new, fresh cells would differentiate, like a fertilized egg would.
1. Differentiation | Single Variable Calculus differentiation English[edit] Etymology[edit] From differentiate + -ion, from different + -iate, from differ + -ent, from Middle English differen, from Old French differer, from Latin differō (“carry apart, put off, defer; differ”), from dis- (“apart”) + ferō (“carry, bear”); cognate with Ancient Greek διαφέρω (diaphérō, “to differ”). Pronunciation[edit] Rhymes: -eɪʃən Noun[edit] differentiation (countable and uncountable, plural differentiations) The act of differentiating.The act of distinguishing or describing a thing, by giving its different, or specific difference; exact definition or determination.The gradual formation or production of organs or parts by a process of evolution or development, as when the seed develops the root and the stem, the initial stem develops the leaf, branches, and flower buds; or in animal life, when the germ evolves the digestive and other organs and members, or when the animals as they advance in organization acquire special organs for specific purposes. Translations[edit]
Differentiation - Everyday Mathematics Differentiation The 2007 edition of Everyday Mathematics provides additional support to teachers for diverse ranges of student ability: In Grades 1-6, a new grade-level-specific component, the Differentiation Handbook, explains the Everyday Mathematics approach to differentiation and provides a variety of resources. The Teacher's Lesson Guide now includes many notes and suggestions that will help teachers differentiate instruction for diverse populations. Every lesson summary includes a list of Key Concepts and Skills addressed in the lesson. This list highlights the range of mathematics in each lesson so that teachers can better use the materials to meet students' needs. Finally, while the curriculum can provide general suggestions for modification, teachers must use their own professional judgment to adjust the curriculum to meet individual needs. Additional Resources Related Links Everyday Mathematics and the Common Core State Standards for Mathematical Practice Grade-Level Information
Differentiated instruction Differentiated instruction and assessment (also known as differentiated learning or, in education, simply, differentiation) is a framework or philosophy for effective teaching that involves providing different students with different avenues to learning (often in the same classroom) in terms of: acquiring content; processing, constructing, or making sense of ideas; and developing teaching materials and assessment measures so that all students within a classroom can learn effectively, regardless of differences in ability.[1] Students vary in culture, socioeconomic status, language, gender, motivation, ability/disability, personal interests and more, and teachers must be aware of these varieties as they plan curriculum. Brain-based learning[edit] Differentiation is rooted and supported by literature and research about the brain. As Wolfe (2001) argues, information is acquired through the five senses: sight, smell, taste, touch and sound. Pre-assessment[edit] Ongoing assessment[edit]
Differentiation rules Rules for computing derivatives of functions Elementary rules of differentiation[edit] Unless otherwise stated, all functions are functions of real numbers (R) that return real values; although more generally, the formulae below apply wherever they are well defined[1][2] — including the case of complex numbers (C).[3] Constant term rule[edit] For any value of , where , if is the constant function given by , then Proof[edit] Let and . This shows that the derivative of any constant function is 0. Intuitive (geometric) explanation[edit] The derivative of the function at a point is the slope of the line tangent to the curve at the point. In other words, the value of the constant function, y, will not change as the value of x increases or decreases. Differentiation is linear[edit] For any functions and any real numbers , the derivative of the function with respect to is: In Leibniz's notation this is written as: Special cases include: The constant factor rule The sum rule The difference rule The product rule[edit]
Differentiate | Definition of Differentiate by Merriam-Webster differentiated; differentiating 1mathematics : to obtain the mathematical derivative (see 1derivative 3) of 2 : to mark or show a difference in : constitute a contrasting element that distinguishes features that differentiate the twins how we differentiate ourselves from our competitors 3 : to develop differential or distinguishing characteristics in What differentiated a laborer from another man … —Sherwood Anderson 4biology : to cause differentiation (see differentiation 3b) of in the course of development cells that are differentiated from stem cells 5 : to express the specific distinguishing quality of : discriminate differentiate poetry and prose 1 : to recognize or give expression to a difference difficult to differentiate between the two 2 : to become distinct or different in character 3biology : to undergo differentiation (see differentiation 3b) when the cells begin to differentiate differentiability play \-ˌren(t)-sh(ē-)ə-ˈbi-lə-tē\noun differentiable play \-ˈren(t)-sh(ē-)ə-bəl\adjective
Calculus/Differentiation/Differentiation Defined What is Differentiation?[edit] Differentiation is a process of finding a function that outputs the rate of change of one variable with respect to another variable. Informally, we may suppose that we're tracking the position of a car on a two-lane road with no passing lanes. . is dependent on time, or . which represents the car's speed, that is the rate of change of its position with respect to time. Equivalently, differentiation gives us the slope at any point of the graph of a non-linear function. is the slope. , the slope can depend on ; differentiation gives us a function which represents this slope. The Definition of Slope[edit] Historically, the primary motivation for the study of differentiation was the tangent line problem: for a given curve, find the slope of the straight line that is tangent to the curve at a given point. The solution is obvious in some cases: for example, a line is its own tangent; the slope at any point is . , the slope at the point is ; the tangent line is horizontal.
Differentiation (Finding Derivatives) By M Bourne In this Chapter 1. Limits and Differentiation 2. See also the Introduction to Calculus, where there is a brief history of calculus. What is Differentiation? Differentiation is all about finding rates of change of one quantity compared to another. What does this mean? Constant Rate of Change First, let's take an example of a car travelling at a constant 60 km/h. We notice that the distance from the starting point increases at a constant rate of 60 km each hour, so after 5 hours we have travelled 300 km. Rate of Change that is Not Constant Now let's throw a ball straight up in the air. Now let's look at the graph of height (in metres) against time (in seconds). Notice this time that the slope of the graph is changing throughout the motion. The slope of a curve at a point tells us the rate of change of the quantity at that point. positiveslopenegativeslopeGraph of ball height showing slope. Important Concept - Approximations of the Slope slope=x2−x1y2−y1 Why Study Differentiation?
Differentiation - Biology-Online Dictionary Definition noun (developmental biology) The normal process by which a less specialized cell develops or matures to become more distinct in form and function (medicine) The determination of which among the diseases with similar symptoms is the one that the patient is suffering, especially through a systematic method Supplement Differentiation in (developmental biology) refers to the normal process by which a less specialized cell undergoes maturation to become more distinct in form and function. In medicine, the term differentiation pertains to the determination of which among the diseases with similar symptoms is the one that the patient is suffering, especially through a systematic method. See also: dedifferentiation Related term(s): cell differentiation Related form(s):
What Is Differentiated Instruction? Click the "References" link above to hide these references. Csikszentmihalyi, M. (1997). Finding Flow: The Psychology of Engagement with Everyday Life. New York: Basic Books. Danielson, C. (1996). Sternberg, R. Tomlinson, C. (1995). Tomlinson, C. (1999). Vygotsky, L. (1986). Winebrenner, S. (1992).