Difference quotient calculator with steps
Difference quotient calculator
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Are you struggling with finding the Difference quotient of a mathematical expression? Look no further! Our Difference quotient calculator with steps is here to help. With this tool, calculating the Difference quotient for any given function is just a few clicks away.
To use the calculator, simply follow these three easy steps:
- Input the mathematical expression in the provided text field.
- Select the variable for which you wish to calculate the Difference quotient.
- Click the “Calculate” button. Once you do, a window will appear with a step-by-step explanation of the solution.
It’s that easy! Start using our Difference quotient calculator today and make your mathematical calculations a breeze.
What is the difference quotient?
The difference quotient formula
The difference quotient is a mathematical concept used to measure the rate of change of a function f(x) with respect to x over a given interval [x, x+h]. It is calculated by finding the slope of the secant line that intersects the curve y=f(x) at two points: (x, f(x)) and (x+h, f(x+h)).
How to find the difference quotient
Next we will show you how to find the difference quotient using an example generated with the help of our Difference quotient calculator:
The difference quotient is given by
f(x+h)−f(x)h e.1
To find f(x+h), plug x + h instead of x:
f(x+h) = x+h(x+h)+3
Finally we substitute the values of f(x+h) and f(x) into e.1:
f(x+h)−f(x)h = x+h(x+h)+3 − xx+3 h
f(x+h)−f(x)h = 3(x+3+h)·(x+3)
The difference quotient examples
Example 01: difference quotient of 1/x
f(x+h)−f(x)h
f(x+h) = 1x+h
f(x+h)−f(x)h = 1x+h − 1x h
f(x+h)−f(x)h = −1x·(x+h)
Example 02: difference quotient of x2/(x2+3x)
f(x+h)−f(x)h
f(x+h) = x+h(x+h)2+3·(x+h)
f(x+h)−f(x)h = x+h(x+h)2+3·(x+h) − xx2+3·x h
f(x+h)−f(x)h = −1(x+3+h)·(x+3)