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# Derivative Calculator

Derivative calculator helps to compute the derivative of a given function. Differentiation is a fundamental concept in calculus. It is the process of finding the derivative of a function. The changing relationship between two variables can be determined by using differentiation.

## What is a Derivative Calculator?

Derivative calculator is an online tool that helps to differentiate a function and find its derivative. Differentiation can be defined as a small rate of change in one quantity (dependent variable) with respect to another quantity (independent variable). To use this * derivative calculator*, enter the value in the input box.

### Derivative Calculator

## How to Use Derivative Calculator?

Please follow the steps mentioned below to find the derivative using the online derivative calculator:

**Step 1:**Go to Cuemath’s online derivative calculator.**Step 2:**Enter the function, f(x), in the given input box.**Step 3:**Click on the**"Calculate"**button to find the derivative of the function.**Step 4:**Click on the**"Reset"**button to clear the field and enter new values.

## How Does Derivative Calculator Work?

There are many real-life applications of differentiation. For example, the speed of an object can be calculated as the rate of change of distance with respect to time. Further, we can also find the slope of a line or a curve using the concept of differentiation. The maximum and minimum values of various functions can also be determined by differentiating them. If we have a differentiable function y = f(x), then f'(x) or dy/dx is used to represent the first-order derivative. If a function is differentiable, it implies that the function is also continuous. However, the converse is not true. This means that a continuous function might not be differentiable. To compute the derivative of a function using limits, we can apply the first principle of differentiation. The formula can be given as:

f'(x) = \(\lim_{\Delta x\rightarrow 0}\frac{f(x + \Delta x) - f(x))}{\Delta x}\)

Using this formula we can derive a differentiation formula that can be applied to elementary functions. This is given as follows:

If f(x) = x^{n}

Then,

f'(x) = nx^{n - 1}.

There are certain important rules that must be followed while differentiating a function. These are given below:

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## Solved Examples on Derivatives

**Example 1:** Find the derivative of 5x^{3} + 2x^{2} and verify it using the derivative calculator.

**Solution:**

f(x) = 5x^{3} + 2x^{2}

f'(x) = d / dx( 5x^{3} + 2x^{2})

f'(x) = d / dx ( 5x^{3}) + d / dx(2x^{2})

f'(x) = 5 . d / dx (x^{3}) + 2 . d / dx (x^{2})

f'(x) = 5 (3x^{2}) + 2( 2x)

f'(x) = 15x^{2} + 4x.

**Example 2:** Find the derivative 13x^{2} + 8 and verify it using the derivative calculator.

**Solution:**

f(x) = 13x^{2} + 8

f'(x) = d / dx( 13x^{2} + 8)

f'(x) = d / dx ( 13x^{2}) + d / dx(8)

f'(x) = 13 . d / dx (x^{2}) + d / dx (8)

f'(x) = 13 (2x) + 0

f'(x) = 26x

Similarly, you can use the derivative calculator to find the derivatives of the following functions:

- x
^{3}/2 - 5x
^{2}+ 6x^{7}

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