foundations of differential calculus

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, medicine and computer sci..

>does not exist, then we say that the function is not differentiable. If the above limit exists, we say the function f(x) is differentiable. In order to test the differentiability of a function at a point, the right hand derivative and left hand derivatives are introdu..

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..

Definitions - Differential Equation: A differential equation is a relation between the independent, dependent variables and their differential coefficient..

Logarithmic Differentiation - When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation.When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation. Let y = f(x) g(x) Ta..

Differentiation of certain functions seem to be very difficult, but by suitably substituting the independent variable with some trigonometric function or other functions, they can be differentiated easily. If f(x) involves inverse trigonometric functions of algebraic..

When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation. Let y = f(x) g(x) Taking log on both sides, we have logy = g(x) logf(x). Differentiating with respect to x, we get, ..

Differentiation by Substitution - Differentiation of certain functions seem to be very difficult, but by suitably substituting the independent variable with some trigonometric function or other functions, they can be differentiated easily.Differentiation of c..

Approximations by Differentials - Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d ..

Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d ..