# Elementary Rules Of Differentiation

The different Elementary Rules of differentiation are used to solve different Differential Equations

According to elementary rules of differentiation there are following formulas:

1. d (x^n) /dx = n . x^(n-1), where n is any number.

2. d (e^x )/dx = e^x.

3. d (c) /dx = 0, where c is any constant.

The following are the general rules of differentiation:

1. Derivative of Addition of two Functions: d(u + v)/ dx = du/dx + dv/dx.

2. Derivative of Difference of two Functions: d(u - v)/ dx = du/dx - dv/dx.

3. Derivative of Product of two functions: d(u * v)/ dx = (du/dx) * (dv/dx).

4. Derivative of Quotient of two functions: d(u / v)/ dx =v. du/dx - u. dv/dx/v^2.

## Differentiation is Linear

Differentiation is a process of finding the derivative of a function. Whenever we deal with Precalculus or Calculus we have to deal with differentiation. If we call differentiation as the heart of the calculus then it won't be wrong. Let's start with the Physical Significance of differentiation.

Let s = f( t ) -----(1), be any function which represents ...Read More

## Product rule

While studying differentiation, we have to strictly follow certain rules of differentiation, to solve the different types of equations. In the section you will learn different concepts of the product rule of differentiation. According to the, product rule of differentiation we can say that,

d (u.v)/ dx = u . dv/dx  + v . du/dx

In this, if 'u' & 'v' are any Func...Read More

## Chain Rule

The chain rule was first used to calculate the differentiation of the expression

(m+nx+lx2)

The chain rule was used but this did not come out as a stand-alone rule.

L'hospital rule also uses this rule but it is not a standalone rule to imply explicitly on equations.

The rule was defined a standalone rule by Lagrange’s theory of function analytics.

## Inverse function rule

In Inverse differentiation, any function is invertible if it can be represented in the form of Inverse Function. So, we have to first understand about inverse Functions and also about inverse function rule. A function is invertible if it is One-to-One. One-to-one means there are two different values x1 and x2 such that: x1!=x2 and this implies that f(x1)!=f(x2)....Read More