## Introduction to First Derivative Calculator

A first derivative calculator is an online tool that can calculate the first derivative of a function in just a few seconds. It uses the first principle or the delta method to calculate the derivative and provide step-by-step results. It also provides you with all possible intermediate steps.

Derivative and integration are two significant concepts of calculus that deal with the continuous rate of change. We introduce you to our advanced and brilliant tool that assists you in finding the instantaneous rate of change in a function or a quantity with respect to an independent variable.

## The formula used by First Principle Derivative Calculator

The first derivative is calculated by finding the derivative of a function one time. The first principle is used to differentiate a function. It says that if there is a change in a function f(x) due to the change in the independent variable x, then it is written as:

$f’(x)=\lim_{\delta x\to 0}\frac{f(x+δx)-f(x)}{δx}$

Where the rate of change in f(x) is calculated as f' (x), sometimes, it also refers to the slope of a curved line. It is because it calculates the rate of change at a specific point on the curved line.

The first derivative calculator uses the above formula. It allows you to find derivative functions without solving its long-term manual calculations. Using this tool online can help you to learn and practice derivatives at the same time.

Related: Also use our derivative graph calculator to draw a graph indicating the rate of change.

## How to use the First Partial Derivative Calculator?

This tool requires an input function and the differentiation variable to provide a derivative. To provide input values, use the following simple steps;

- In the first step, you need to enter the function. This step requires a function for which you want to calculate the rate of change.
- Now select the variable by which you want to differentiate the given function.
- Now select a number from the time menu. You can select how many times you want to differentiate a function in this step. You can also select 2 to calculate the 2nd derivative.
- Review the function and click the calculate button.

After clicking the calculate button, the first partial derivative calculator will provide you with the derivative of the given function within a few seconds. You can also get a third derivative if you select three from the time menu. This tool will also provide you with a plot of the given function so you can learn its rate of change.

## Why use the First Order Derivative Calculator?

The **derivative calculator** has made the calculations and concepts of derivatives easy for you. With this tool, you can learn more about differentiation with visual plots. It is an advancement in learning mathematics online so students and mathematicians can practice more in less time.

While calculating the derivative of a function, you may need help with tricky calculations as it involves the delta method. Moreover, sometimes you must differentiate a function more than once, i.e., the nth derivative. Therefore, it would be best for you to use the first implicit derivative calculator because it follows all requirements of an online math tool.

## Benefits of using the first implicit derivative calculator

This online calculator has many benefits you can get by using it for knowledge and calculations. Some of the other benefits of this tool are listed below.

- This tool is best to calculate the nth derivative of a function.
- It can handle any function, whether in the form of a combination or product of two or more functions.
- It is easy to use as you must perform only a few steps.
- It saves your time and energy from doing tricky and long-term calculations.
- It uses the product rule of derivatives to calculate the derivative of the product of two functions.

## Frequently asked questions

### What is the first derivative?

The first derivative of a function expresses the slope of a tangent line to the curve at any point because a function's first derivative tells us a lot about the function, whether it is increasing or decreasing.

### What does 1st and 2nd derivative mean?

The slope of the graph at a point is represented graphically by the first derivative. The second derivative calculator indicates whether the curve is concave up or down at that point. The graph bends upward at a point where the second derivative is positive.

### Is the first derivative the same as slope?

Yes, the first derivative is the same as the slope of the tangent line calculator. It is because it calculates the rate of change in the function's graph at a point when the function is changing.

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