Introduction to Derivative at a Point Calculator:
Derivative at a point calculator is an online tool that helps you to find derivative at a point of a function. It evaluates the behavior of a given derivative function at a certain point on a graph.
The derivative calculator at a point is the best online source for students, teachers or engineers who want to get an understanding of how to measure the instantaneous rate of change and plot it on a graph after calculation.
What is Derivative at a Point?
The derivative at a point is a process of finding the instantaneous rate of change of a function at a specific point on the graph. It uses the formula of the limit definition of the derivative to find the attribute of that given function at point a.
It also helps you to find slope of the tangent line on a graph to know the insight of a function, whether it is concave up or concave down in the XY graph.
Formula of Derivative at a Point:
It can be expressed mathematically asa function f(x), the derivative at x = a is denoted f′(a) or df/d x∣x = a. The formula used by the derivative at a point calculator is:
$$ f’(a) \;=\; \lim_{h \to 0} \frac{f(a + h) - f(a)}{h} $$
How to Find the Derivative at a Point?
To find derivative at a point of both graphical and algebraic methods, the derivative at point calculator follows some usual derivation methods to give you the solution. Here is a detailed, step-by-step guide on how to calculate the derivative at a point.
Step 1:
Determine the function f(x) and given point value a.
Step 2:
Put the value of given function in definition of limit derivative formula.
Step 3:
Simplify the given expression and apply the limit.
Step 4:
Plot the graph of function f(x) and draw a tangent line at x = a on the graph.
Solved Example of Derivative at a Point:
An example of a derivative at a point along with its solution is given below to let you know how the derivative at a point calculator gives the solution of the derivative at a point problem.
Example:
For the function given by f(x) = x - x2, use the limit definition of derivative to determine f’(2).
Solution:
Identify the given function f(x) such as,
$$ f(x) \;=\; x - x^2 $$
Put the point x = 2 into the given function f(x),
$$ f(2) \;=\; 2 - 2^2 \;=\; -2 $$
$$ f(2 + h) \;=\; (2 + h) - (2 + h)^2 $$
The formula of limit derivative function,
$$ f’(a) \;=\; \lim_{h \to 0} \frac{f(a + h) - f(a)}{h} $$
Put the values in the limit derivative formula such as,
$$ f’(2) \;=\; \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h} $$
$$ f’(2) \;=\; \lim_{h \to 0} \frac{(2 + h) - (2 + h)^2 - (-2)}{h} $$
Simplify the above expression,
$$ f’(2) \;=\; \lim_{h \to 0} \frac{2 + h - 4 - 4h - h^2 + 2}{h} $$
$$ f’(2) \;=\; \lim_{h \to 0} \frac{-3h - h^2}{h} $$
$$ f’(2) \;=\; \lim_{h \to 0} (-3 -h) $$
Apply limit to get solution at a specific point,
$$ f’(2) \;=\; -3 $$
Therefore the f`′(2) is the instantaneous rate of change of f at the point (2, −2) and its visual representation is,
PASTE THE GRAPH HERE!
How to Use Derivative at a Point Calculator?
The derivative calculator at a point has a user-friendly interface, so you can easily use it to evaluate the given function derivation at a point solution. Before adding the input value problems, you must follow some simple steps. These steps are:
- Enter the given derivation function f(x) in the input field that you want to evaluate for differentiation at a point value.
- Add the derivative variable on which your function is differentiated for a specific point in the input field.
- Recheck your input value for the given derivative at a point problem solution before hitting the calculate button to start the calculation process in the derivative at point calculator.
- Click on the “Calculate” button to get the desired result of your given derivative at a point problem.
- If you want to try out our point differential calculator to check its accuracy in solution, use the load example to get the solution
- Click on the “Recalculate” button to get a new page for solving more derivative at a point questions with solutions.
Output from Derivative Calculator at a Point:
Derivative at a point Calculator gives you the solution to a given derivative problem when you add the input value to it. It provides you with solutions that may contain as:
- Result Option:
You can click on the result option as it provides you with a solution to derivative at a point value questions.
- Possible Step:
When you click on the possible steps option then the point differential calculator provides you with the solution of the differential problem at a specific value in step.
- Plot Option:
Plot option provides you solution in the form of a graph for a visual understanding of the derivative function at a certain point
Benefits of Derivative at Point Calculator:
The dy/dx at a point calculator gives you multiple useful features that you avail whenever you use it to calculate derivative at a point problems and to get solution. These features are:
- Our derivative calculator at a point saves the time and effort that you consume in solving differential questions at x = a to get solutions in a few seconds.
- It only takes the input of your function and you get a solution even it is for a complicated derivation function at a particular point.
- Derivative at a point Calculator will give you results when you are computing differentiation of a function at a point easily without taking any manual calculation guide so there is no chance of mistakes in the solution.
- It is a free-of-cost tool that provides you with a solution for a given derivation function to evaluate derivative at a point using the differential rules on a graph without spending.
- The point differential calculator is an adaptive tool that allows you to find the different types of multivariable derivation.
- You can use this Calculator for practice to get familiar with this concept of derivative function at a specific point.
- Our Calculator is a trustworthy tool that provides you with precise solutions as per the given derivative problem at a point.
