derivative of a function in general

Which of the following is correct for a function that is differentiable at a point x = 3 ? => left hand side derivative = right hand side derivative at x = 3 or left hand side derivative may not be equal to the right hand side derivative at x = 3 or..

We have already defined the derivative of a function f(x) at a particular point 'a' and derivative of f(x) in general for the variable x as f (a) and f (x) respectively. The restriction in both the cases is that 'the limit must exist'. IfWe have already defin..

A differential equation is said to be linear when the dependent variable and its derivatives occur in the first degree and are not multiplied together. When f 1 to f n as the functions of x, in general linear differential equations of order ..

They consist of repeat units of monosaccharides or their derivatives. These units are held by glycosidic bonds. These carbohydrates liberate large number of monosaccharide molecules on hydrolysis. They are colorless and tasteless. So, they are called non-sugars. They are concerned with tw..

Two molecules of an aldehyde or a ketone having at least one a -hydrogen atom condense in the presence of a dilute acid to give a b -hydroxyaldehyde or b -hydroxy - ketone. This reaction is called aldol condensation. The name is derived from the names of two functional group..

Consider the function f (x) = x 2 + Ax + B Clearly (x) is a solution of the differential equation. y''= 2, because if the second derivative of f (x) gives 2. That is y = x 2 + Ax + B is a general solution of the differential equation. y'' = 2 Each value of A and ..

The hydroxy derivatives of aliphatic hydrocarbons (compounds having their carbon atoms in chains and not in the form of rings) are called alcohols. When one, two or more hydrogen atoms of a hydrocarbon are replaced by a corresponding number of hydroxyl groups (-OH), alcohols can be obtain..

This chapter contains oxygen compounds in which oxygen is bonded to a carbon atom through a double bond. The functional unit >C = O, present in these compounds is called carbonyl group. We limit our study now to compounds having an acyl group (R - C = O) is bonded to hydrogen, carbon,..

The quantitative relationships between different species in the redox reactions gives its stoichiometry. These relationships are derived in the same manner as derived for general chemical equations after writing the balanced redox equati..

Introduction - Integration and differentiation are a pair of inverse operations. So far, from a given function, we have been finding its derivative but the question arises: what is the function whose derivative is known? If the derivative of a ..