derivative of implicit functions

Structures of Functional Groups Present in Carboxylic Acid Derivatives - The structure of the functional groups in acyl halide, acid anhydride, ester and amide are similar to that of the carboxyl group. Due to the presence of lone pairs of electrons at the halogen, oxy..

Replacement of hydroxyl group in carboxylic acids with a halogen, carboxylate, alkoxy or amino group gives functional derivatives of carboxylic acid known as acyl halides, acid anhydrides, esters or amides respectivel..

Let f(x) = k be the given function. Then, we have Therefore derivative of a constant is 0. or..

The structure of the functional groups in acyl halide, acid anhydride, ester and amide are similar to that of the carboxyl group. Due to the presence of lone pairs of electrons at the halogen, oxygen and nitrogen atoms, resonance is possible in these derivatives just like ..

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 aromatic (Ar-COOH) depending on whether -COOH group is a..

Let f be a function of x (y=f(x)). Let a be a point in the domain of f. The RHD of f at a is defined as where h>0, provided the limit exist..

Let f be a function and a be any point in its domain. Let h>0 be a small number. f(x) is said to be differentiable if exists and is denoted by f | (a), then f | (a) is called the derivative or differential coefficient of f(x) at x = a. That ..

Derivability implies continuity Derivative of a constant function is zero. ..

Let f be a differentiable function on an interval I and let a I. Let f "(a) be continuous at a. Then i) 'a' is a point of local maxima if f '(a) = 0 and f "(a) < 0 ii) 'a' is a point of local minima if f '(a) = 0 and f "(a) > 0 iii) The test fails if f '(a) = 0 and f "(a) = 0. In th..

The equation that involves one (or) more derivatives of some unknown functions which are required to be found is called => Non linear equation or Differential equation or Linear equation or Quadratic equation..