derivations


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Fundamental and Derived Units
The units of fundamental physical quantities are called fundamental units. They are m, kg and sec. These units can neither be derived from one another nor can be resolved into other units. They are independent to each other. Units of physical quantities can be expressed in terms of funda..
Application of Derivatives Introduction
Introduction - Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a he..
Right Hand Derivative
as x approaches a through values greater than 'a' is called Right hand derivative at x = a, denoted by Rf '(a)...
Naming Benzene Derivatives
nomenclature for two monovalent substituents on benzene ring Only one kind of monosubstituted derivatives are possible in benzene rings as all six hydrogen atoms are equivalent. For example, there is only one toluene. It does not matter where the methyl group is attached because all the following arrangements are equivalent. When two same or diff..
Derivatives of Second Order
Similarly, higher order derivatives can also be define..
Derivative of Inverse Trignometric Functions
Derivative of Inverse Trignometric Functions - Before finding the differentiation of inverse trigonometric functions, recall how the inverse trigonometric functions are defined and what the domain and range of each inverse trigonometric function. For ready reference, the domain and range ..
Carboxylic Acids and its Derivatives - Introduction
functional formula of carbonyl group Carboxylic Acids and its Derivatives - Introduction - Carbon compounds containing a carboxyl functional group -COOH are called carboxylic acids. A carboxyl group is constituted of two groups - a carbonyl group and a hydroxyl group -OH. Carboxylic acids may be aliphatic (R-COOH) or aromati..
Some of the Common derived units
Quantity Derivation of the Quantity SI Unit Symbol Area Length square m 2 Volume Length cube m 3 Density Mass per unit volume kg m -3 Speed Distance travelled per unit time m S -1 Acceleration Speed change p..
Application of Derivatives Summary
x = a is called a point of inflexion. Rolle's theorem: If a function f(x) is such that (i) f (x) is continuous on [a,b] (ii) f (x) is differentiable on (a,b) and (iii) f (a) = f (b) Geometrical interpretation of Rolle's theorem Let AB be the graph of y = f(x) such that A = (a , f(a)) and B = (b , f..
Polyhalogen Derivatives - Carbon tetrachloride
Many polyhalogenated hydrocarbons find important use as industrial solvents, pesticides, refrigerants, medicines, inert lining of cooking utensils, etc. Some useful chloro compounds a..
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