## Introduction to Differential Calculus

In the seventeenth century, Sir Isaac Newton, an English mathematician (1642–1727), and Gottfried Wilhelm Leibniz, a German mathematician (1646–1716), considered... Click here to read more

From basic to higher mathematics

In the seventeenth century, Sir Isaac Newton, an English mathematician (1642–1727), and Gottfried Wilhelm Leibniz, a German mathematician (1646–1716), considered... Click here to read more

A variable which can assign any value independently is called the independent variable, and the variable which depends on some independent... Click here to read more

Example: Let (a) Find the average rate of change of with respect to over the interval . (b) Find the... Click here to read more

Let be a given function of . Give to a small increment and let the corresponding increment of by ,... Click here to read more

Example: Find, by definition, the derivative of function with respect to . Solution: Let I. Change to and to II.... Click here to read more

The derivative of a constant function is zero. Now we shall prove this constant function with the help of definition... Click here to read more

The derivative of x is 1 (one). Now by definition or first principle we shall show that derivative of x... Click here to read more

Power Rule of derivative is an essential formula in differential calculus. Now we shall prove this formula by definition or... Click here to read more

It is given that two functions are in form and take derivative of sum of these two functions which is... Click here to read more

It is given that two functions are in form and take derivative of difference of these two functions which is... Click here to read more

To find a derivative of a function, consider the examples to elaborate the concept of derivative of a given function... Click here to read more

To find a derivative of square roots of a function. This can be proving by using derivative by definition or... Click here to read more

Product rule of derivative is . In words we can read as derivative of product of two functions is equal... Click here to read more

Product rule of derivative is . In words we can read as derivative of quotient of two functions is equal... Click here to read more

Composition of Two Functions: The composition of two functions and is defined as Chain Rule: If is differentiable at the... Click here to read more

Example 1: Differentiate with respect to using chain rule method. Let us consider , then . Applying chain rule, we... Click here to read more

In this tutorial we discuss basic formulas of differentiation for algebraic function. 1. , Where is any constant. 2. 3.... Click here to read more

We shall prove formula for derivative of sine function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of cosine function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of tangent function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of cotangent function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of secant function using by definition or first principle method. Let us suppose that... Click here to read more

We shall prove formula for derivative of cosecant function using by definition or first principle method. Let us suppose that... Click here to read more

In this tutorial we shall discuss derivative of sine squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of cosine squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of tangent squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of cotangent squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of secant squared function and its related examples. It can be proved by... Click here to read more

In this tutorial we shall discuss derivative of cosecant squared function and its related examples. It can be proved by... Click here to read more

In trigonometric Differentiation most of the examples based on sine square roots function, we will discuss in detail derivative of... Click here to read more

In this tutorial we discuss basic formulas of differentiation for trigonometric functions. 1. 2. 3. 4. 5. 6. For remember... Click here to read more

In this tutorial we shall be concerned with the derivative of inverse trigonometric functions and first we shall prove sine... Click here to read more

In this tutorial we shall be concerned with the derivative of inverse trigonometric functions and first we shall prove cosine... Click here to read more

In this tutorial we shall explore the derivative of inverse trigonometric functions and we shall prove derivative of tangent inverse.... Click here to read more

In this tutorial we shall explore the derivative of inverse trigonometric functions and we shall prove derivative of cotangent inverse.... Click here to read more

In this tutorial we shall explore the derivative of inverse trigonometric functions and we shall prove derivative of secant inverse.... Click here to read more

In this tutorial we shall explore the derivative of inverse trigonometric functions and we shall prove derivative of cosecant inverse.... Click here to read more

In this tutorial we discuss basic formulas of differentiation for inverse trigonometric functions. 1. 2. 3. 4. 5. 6. For... Click here to read more

A function defined by , where , is called the logarithm of to the base . The natural logarithmic function... Click here to read more

A function defined by , where , is called the logarithm of to the base . The common logarithmic function... Click here to read more

If is a complicated function, i.e. it involves several products of functions, quotients or radical signs, then we take logarithms... Click here to read more

In this tutorial we discuss basic differentiation formulas of logarithmic functions. 1. 2. Now general logarithmic formulae when any function,... Click here to read more

Example: Differentiate with respect to . Consider the function Differentiate both sides with respect to , we have Example: Find... Click here to read more

In this tutorial we shall find the derivative of exponential function. We prove the general rules for differentiation of exponential... Click here to read more

In this tutorial we shall find the derivative of exponential function . We prove the general rules for differentiation of... Click here to read more

In this tutorial we discuss basic differentiation formulas of exponential functions. 1. 2. Now general exponential formulae when any function,... Click here to read more

Example: Differentiate with respect to . We have given function Now differentiate both sides with respect to Using the derivative... Click here to read more

In this tutorial we shall study certain combination of and , called hyperbolic functions. These functions have numerous applications and... Click here to read more

In this tutorial we shall prove derivative of hyperbolic sine function. Let the function of the form By definition of... Click here to read more

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