## 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 - x^{2}, 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.