derivative of a function in general

Which of the following is the derivative of the function f ( x ) = x x 2 + 1 6 + 1 6 sin h - 1 ( x 4 ) ? => 2 x 2 + 1 6 or 1 6 + x 1 6 + x 2 or 3 2 + 2 x 2 + 6 4 2 x 2 + 1 6 or 1 + x 2 + 1 6 or 3 2 x 2 + 1 6..

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'. If does n..

Differentiability - 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'. IfW..

The word root represents the number of carbon atoms in the parent chain and it is the basic unit of the name. The parent chain is selected as per the longest chain rule i.e., the parent chain is the longest continuous chain of C-atoms including the functional group and the multiple bonds..

Polysaccharides - Introduction - 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-s..

Aldol condensation - 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 func..

The functional group is an atom, or a group of atoms which can replace one or more hydrogen/s in a hydrocarbon. This group when present in organic compounds defines the characteristic physical and chemical properties of that particular family of organic compounds. Thus a functionalh..

Alcohols - 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 ca..

Introduction - 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 hyd..

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 functionh..