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