## Factorial of 0, Proof and Examples

Factorial of 0 Proof: since we know that where n belongs to positive integer Examples. Now we will prove that Factorial of 0 equal to

## Power rule of differentiation, Theorem Example’s Solution

Power rule of differentiation Prove that: ; .

## Euler’s Theorem, Proof and Examples

Euler’s Theorem Statement: If is a homogeneous function of of degree , then . Proof: we have ,Therefore . . and . . Thus from

## Logarithmic Differentiation and its Examples with Solution

Logarithmic Differentiation: Let where both and are variables or function of , the derivative of can be obtained by taking natural logarithms of both of

## Explicit Differentiation and its Examples with Solution

Explicit Differentiation Explicit function: If is easily expressed in term of the independent variables ,Then is called an Explicit function of . Symbolically it is

## Implicit Differentiation, Example’s Solution

Implicit Differentiation: Implicit functions: If and are mixed up and cannot be expressed in terms of the independent variable , Then is called an Implicit

## Homogeneous Equation with Examples

HOMOGENEOUS EQUATION: Each equation of the system of following linear equations . . . is always satisfied by , so such a system is always

## Sum and Difference Rule of Derivatives

Theorem sum and difference rule of derivatives Let and are differentiable at , Then () and () are also differentiable at and That is also

## Differentiation rule, Theorem examples with solutions

Now we will prove the important formula or rule which are used to determine derivative of different function efficiently. You can prove differentiation in easy

## What is rational number:

We know that a rational number is a number that can be put in the form of where p, q Z and q ≠ 0.