In mathematics, the difference quotient method is used to determine the slope of the secant / curved line, which is between the two different points on the function’s graph. A function is considered a curve or a line with one “y” value for each “x” value. You calculate the difference quotient by utilizing two ways. One of the ways is the manual calculation, and the second one is the use of online difference quotient calculator free tools. In this guidepost, you will learn about how to find the difference quotient.

Difference Quotient Formula

Considering the single variable calculus, the central difference quotient is said to be the name of an expression that takes the limit; when “h” approaches zero, that gives the derivative of the function f. Basically, the difference formula is used to calculate the slope of the line, which passes by the two points. The formula is also used to define the derivative. Instead of using the difference quotient formula, you get the free assistance of an online difference of quotient calculator. The digital difference quotient calculator is a viable option because it calculates the difference quotient for ten functions and shows the step-wise procedure.

If you still want to go for the manual calculation, then use the below-mentioned formula:

** F (x + h) – f(x) / h**

How to Find Difference Quotient

The difference quotient is said to be an important part of mathematics, especially when it comes to calculus. If a function f(x) has two input values x & x + h. Where “h” represents the distance between x and x + h. By considering the formula the difference quotient is said to be the quotient of the values of the function, f(x + h) – f(x) & the difference of the input values of (x + h) – x.

By simplifying the formula f (x + h) – f(x) / (x + h) – x, it will looks like this:

f(x + h) – f(x) / h.

After getting the simplified form of the difference quotient formula, it is time to understand the steps that are involved in the manual calculator for the difference quotient. Whenever we are given the formula, solving the formula is just a matter in which you need to determine the values for the variables & expressions involved in the formula. You just need to insert the values you find and then simplify the values to find the difference quotient. If it seems complicated to you, then you can consider using a difference quotient calculator that measures the slope of the secant line, which passes through two points. To understand the procedure, have a look at the below-mentioned steps.

- Insert x + h into the function and simplify it for finding f(x + h).
- After the simplification you have f(x + h). Now, by plugging f(x + h) & f(x) into it and then simplifying it.
- Now, it’s time to insert the results from step # 2 for the numerator in the difference quotient and simplify it.

If it still seems complicated to calculate the difference quotient using the steps mentioned above, then using a difference quotient solver is a considerable option.

**Final Words**

The difference quotient can be defined as the formula, which can be used to determine the slope of the secant line, which touches the curve at two points. The procedure to measure the slope is somehow difficult to understand. But you have the option to use the online difference quotient calculator whenever you wants to compute the difference quotient. This free online tool shows the results according to the difference quotient formula and the step-by-step procedure.