Introduction to Derivative Graph Calculator:
Derivative graph calculator is an online tool that helps you to find the graph of a given derivative function in a few seconds. Our tool evaluates the rate of change of a function to tell whether it is upward or downward on a graph.
The derivative grapher is a helpful tool for students, teachers, or professionals that provides you a complete knowledge and understanding of graphs and how a function changes at a specific point on a graph in the given interval.
What is the Derivative of a Graph?
The derivative of a graph is a process in calculus that is used to represent the rate of change of a function. It can find the slope of a tangent line on a graph at a specific point. It is known as the derivative of a graph or slope of a tangent line curve.
This method converts the numerical value into a visual representation on a graph. It is not only give you a solution on a graph but also tells whether the function is increasing or decreasing order in a given interval.
Formula of Derivative on a Graph:
The formula of a derivative on a graph is used to find the rate of change of a function with the help of the definition of the derivative. The formula used by the derivative graph calculator is,
$$ f’(x) \;=\; \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} $$
- f(x) is the given function for derivation
- f(x+h) is the rate of the change
- f`(x) is the derivative of a given function
How to Find the Derivative of a Graph?
To find the derivative of a graph you need to understand the working method of derivative graphing calculator on a graph in steps to analyze the rate of change of a function that varies across different points on the graph. Let's see a stepwise guide to finding the derivative function on a graph.
Step 1:
Identify the given function f(x) around which the rate of change is found.
Step 2:
Put the function f(x) into the formula of the definition of differentiation.
Step 3:
Solve the function after adding value to it, then apply limits.
Step 4:
Put the result of the derivative function equal to zero to find the point value of x.
Step 5:
On the graph use the point value of x to represent the given function on a graph.
Solved Example of Derivative Graph:
An example of directional graph is given to let you know how the derivative graph calculator calculates the directional derivative problem easily.
Example: Calculate the derivative of the function:
$$ f(x) \;=\; x^2 - 2x $$
Solution:
The given data is,
$$ f(x) \;=\; x^2 - 2x $$
As per the definition of derivative,
$$ f’(x) \;=\; \lim_{h \to 0} \frac{h(x + h) - f(x)}{h} $$
So,
$$ f(x + h) \;=\; (x + h)^2 - 2(x + h) $$
$$ f(x) \;=\; x^2 - 2x $$
So ,
Put these value in the above formula to find the rate of change of a given function,
$$ f’(x) \;=\; \lim_{h \to 0} \frac{((x + h)^2 - 2(x + h)) - (x^2 - 2x)}{h} $$
Expand the above expression and solve it.
$$ =\; \lim_{h \to 0} \frac{x^2 + 2xh + h^2 - 2x - 2h - x^2 + 2x}{h} $$
$$ =\; \lim_{h \to 0} \frac{2xh - 2h + h^2}{h} $$
$$ =\; \lim_{h \to 0} \frac{h(2x - 2 + h}{h} $$
$$ =\; \lim_{h \to 0} (2x - 2 + h) $$
Apply the limits, the solution we get is,
$$ =\; 2x - 2 $$
For the graphical representation find the derivative of a given function with respect to x,
$$ y \;=\; x^2 - 2x $$
$$ \frac{d}{dx} (x^2 - 2x) \;=\; 2x - 2 $$
Put 2x - 2 = 0
$$ 2x \;=\; 2 $$
$$ x \;=\; 1 $$
So the function represented in a graph at x=1 as,
PASTE THE GRAPH HERE!
How to Use the Derivative Graph Calculator?
The derivative grapher has an easy-to-use interface, so you can easily use it to evaluate the derivative questions at the graph. Before adding the input for the solutions of the derivative graph problem, you must follow our instructions. These instructions are:
- Enter the given derivative graph function value in the input box.
- Enter the variable of derivation in the input box.
- Review your input value of the differential function for the graph in the derivative graphing calculator before hitting the calculate button to start the calculation process.
- Click on the “Calculate” button to get the desired result of your given derivative graph problem.
- If you want to try out our graph derivative calculator to check its accuracy in solution then use the load example.
- Click on the “Recalculate” button to get a new page for solving more derivative graph questions.
Final Result of Derivative Grapher:
The derivative graphing calculator gives you the solution to a given problem when you add the input in it. It provides you with solutions of derivative graph problems. It may contain as:
- Result Option:
You can click on the result option and then the derivative graph calculator provides you with a solution for derivative graph questions
- Possible Step:
When you click on the possible steps option it provides you with the solution of the derivative graph problem where all calculation steps are given in detail.
- Plot Option:
It gives you the solution of derivative function in graph through a graphical representation for visual understanding as well.
Benefits of Using Derivative Graphing Calculator:
The derivative plotter gives you tons of benefits whenever you use it to calculate derivative graph problems and to get its solution immediately. These benefits are:
- Our graph derivative calculator saves the time and effort that you consume in solving complex derivative graph questions in a few seconds.
- It is a free-of-cost tool that provides you solution of a given derivative function to find its graphical representation on a graph without paying a single penny.
- You can use this derivative grapher for practice so that you get a strong hold on this concept.
- It is a trustworthy tool that provides you with accurate solutions as per your input to calculate the derivative graph problem.
- Derivative graph calculator is a handy tool because you can use it online in just one click and get a solution of even a complex derivative graph problem easily.
