differentiate a variable with respect to another variable

Introduction - The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medic..

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'. IfWe have alr..

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 not exist, then we sa..

Quantities such as height, weight, age, amount can have several different values. Quantities which can assume different numerical values are called variables. Variables are of two types: (a) Continuous (b) Discre..

A set of observations is called a called a collection of data. These observations should possess some common characteristics. They are recorded and used for further study. The quantities such as age, height and number of students are called variables..

Introduction to Differentiation - After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the previou..

Let X be a discrete random variable which can assume values x 1 , x 2 , x 3 ,x n with probabilities p 1 , p 2 , p 3 .. p n respectively then (a) Mean of X or expectation of X denoted by E(X) or m is given by (b) Variance of X denoted by s 2 is given ..

A particle is said to move with variable acceleration if its velocity changes by unequal amounts in equal intervals of time. When a particle moves with variable acceleration, then its average acceleration measured for different time intervals is not the same. In the case of ..

random variable is a function which associates a real number to each outcome of a random experiment..

Consider an example. A person was asked to measure the thickness of a coin. He recorded the following readings: (i) 0.2 cm with ruler (ii) 0.23 cm with vernier (iii) 0.231 cm with micrometer The accuracy of thickness of the coin depended on the instrument used for measuring the thickness. Thus the..