The quotient function actually returns the integer part of a division, here there are two arguments, the denominator is the divisor and the numerator is the dividend. The difference quotient calculator by calculator-online.net assists you to determine the difference quotient for a given function. The difference quotient calculator displays stepwise measurements and the slope of the secant line which passes through two points. In this context, you can determine the difference quotient using the formula.

The simplified difference quotient calculator also known as the Newton Quotient and it’s used to find infinitely small increments by online tools. The difference quotient is actually used to find the values at a difference at the rate difference from function. The rate is used to find the velocity, acceleration, and many other functions in Mathematics. The simplified difference quotient calculator makes the task simple and the task easy for the users.

**How to find the difference quotient?**

In calculus the simplify difference quotient calculator is used to measure the slope of the secant/curved line between two different points on the graph of a function. A function is a curve on the line that has one value of “y” for every value of “x”. Therefore the slope defines the derivation of function. In simplest of the words, We can say the quotient measure the rate of the change of function f(x) with respect to the x in a given interval (x,x+h). The simplified difference quotient calculator makes the task easy for us and the users as they can avoid converting the difficult function to find their difference quotient.

**Example of the ****difference quotient:**

**Example1 :**

Consider the function

F(x) = x^2 + 4

Now Formula to find Difference Quotient is:

f(x) = f (x + h) – f (x) / h

Consider the f(x + h),

Insert the x + h instead of x in the function, we get:

f (x + h) = (x + h)^2 + 4

Then,

f(x) = f (x + h) – f (x) / h

f(x) = ((x + h)^2 + 4) – (x^2 + 4)

f(x)=h + 2x

The difference quotient for

f (x) = x^2 + 4 and the f(x)= h + 2x.

## Example2 :

f(x)=x2+10 is going to be written as h+ 2x

The input values is f(x)=x2+10

The formula for the f(x)=[f(x+h)-f(x)]/h

The formula for the f(x)= [(x+h)2+10-(x2+10)]/h

f(x)= x2+h2+2hx-x2+10-10/h

Now by cutting the x2 and -X2 and 10 and 10, we get the remaining values. The remaining values would be the f(x)= h+2x

f(x)= h2+2hx/h

f(x)= h(h+2x)/h

f(x)= h+2x

The formula for the = h+ 2x

**Symmetric Difference Quotient:**

The difference quotient formula and the difference quotient calculator give the approximations of the derivation of a function when we are finding the Symmetric Difference Quotient. There are other difference quotients such as symmetric and one-sided difference quotients for the derivation of the function.

The symmetric derivative can be generated by the difference quotient calculator, the ordinary derivative which is defined as:

h0 frac {f (a + h) – f (a – h)} {2h}

When we are using the function, it is symmetrically differentiable at the particular point “a”. if its derivative exists at that particular point, then the difference quotient calculator provides all the possible values . The expression under the limit is called a symmetric difference quotient.

**The average rate of change as slope?**

The average rate of change is the change in values of the y variables to the change in values of the variables of x of a given function. If the rate of change is linear and constant, then the resultant slope would be a straight line The slope of a different quotient curved line may be negative, positive, zero, or undefined.

**Conclusion:**

The difference quotient calculator for finding the derivative of quotients for various functions. This would make the task of finding the difference quotient in a matter of seconds. This is one of the simple methods to determine the quotient of a function. You can find the difference quotient of linear and the quadratic equation by the difference quotient calculator