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**Nth Derivative Calculator + Online Solver With Free Steps**

An **nth Derivative Calculator** is used for calculating the **nth**** derivative** of any given function. This type of calculator makes complex differential calculations fairly easy by computing the derivative answer in a matter of seconds.

Nth **derivative** of a function refers to the differentiation of the function** iteratively for n times**. It means computing successive derivatives of the specified function for n number of times, where n can be any real number.

The $nth$ derivative is denoted as shown below:

\[ \frac{d^{n}}{dx^{n}} \]

## What Is Nth Derivative Calculator?

An** nth Derivative Calculator** is a calculator that is used for computing the $nth$ derivatives of a function and to calculate the **higher-order derivatives**.

This **calculator** takes away the trouble of manually calculating the derivative of any given function for n times.

Often, we encounter certain functions for which the derivative calculations become quite lengthy and complex, even for the first derivative. The nth derivative calculator is the** ideal solution** for calculating the derivatives for such functions, where $n$ can be 3, 4, and so on.

Taking** iterative derivatives** of a function assists in predicting the **behavior of the function, **over time which is of great significance, especially in physics. The **$nth$ Derivative Calculators** can prove to be quite handy in such situations where the variating behavior of a function needs to be determined.

## How To Use the Nth Derivative Calculator

The **nth Derivative Calculator** is quite simple to use. Apart from its speedy calculations, the best feature of the nth derivative calculator is its **user-friendly interface. **

This calculator consists of **two boxes:** one for inputting the number of times the derivative needs to be calculated, i.e, n, and the other for adding the function. A “**Submit”** button is present just below these boxes, which provides the answer upon clicking.

Given below is a step-by-step guide for using the nth derivative calculator:

### Step 1:

Analyze your function and determine the value of n for which you need to calculate the derivative.

### Step 2:

** **Insert the value of n in the first box. The value of n needs to lie in the domain of real numbers. This value corresponds to the number of differential iterations that need to be performed on the function.

### Step 3:

In the next box, insert your function f(x). There is no restriction on the type of function that needs to be evaluated.

### Step 4:

Once you have entered your value of n and your function, simply click on the button that says** “Submit**.” After 2-3 seconds, your solved answer will appear in the window below the boxes.

## Solved Examples

### Example 1:

Calculate the first, second, and third derivative of the function given below:

\[ f(x) = 3x^{4} + 16x^{2} – 3x \]

### Solution:

In the given question, we need to calculate the first, second, and third derivatives of the function. So, $n$ = $1$, $2$, and $3$.

Calculating the first derivative:

\[ n = 1\]

\[ f’(x) = \frac{d}{dx} (3x^{4} + 16x^{2} -3x) \]

Upon inserting the value of $n$ and $f(x)$ in the $nth$ derivative calculator, we get the following answer:

\[ f’(x) = 12x^{3} + 32x -3 \]

Now calculate the second derivative:

\[ n = 2 \]

\[ f’’(x) = \frac{d^{2}}{dx^{2}} (3x^{4} + 16x^{2} -3x) \]

Upon inserting the value of $n$ and $f(x)$ in the $nth$ derivative calculator, we get the following answer:

\[ f’’(x) = 4(9x^{2} + 8) \]

Now calculate the third derivative:

\[ n = 3 \]

\[ f’’’(x) = \frac{d^{3}}{dx^{3}} (3x^{4} + 16x^{2} -3x) \]

Upon inserting the value of $n$ and $f(x)$ in the $nth$ derivative calculator, we get the following answer:

\[ f’’’(x) = 72x \]

### Example 2:

Find the 7th order derivative of the following function:

\[ f(x) = x. cos(x) \]

### Solution:

In the given question, both the value of $n$ and the function $f(x)$ are specified as below:

\[ n = 7 \]

And:

\[ f(x) = x.cos(x) \]

The question demands to calculate the 7th order derivative of this function. For doing so, simply insert the values of $n$ and the function $f(x)$ in the $nth$ derivative calculator. The answer turns out to be:

\[ f^{7} (x) = \frac {d^{7}}{dx^{7}} (x.cos(x)) \]

\[ \frac {d^{7}}{dx^{7}} (x.cos(x)) = x.sin(x) – 7 cos(x) \]