The derivative calculator is a free online tool that displays the derivative of the given function. BYJU’S online derivative calculator or differentiation calculator tool makes the calculations faster, and it shows the first, second, third-order derivatives of the function in a fraction of seconds.

## How to Use the Derivative Calculator?

The procedure to use the derivative calculator (differentiation calculator) is as follows:

**Step 1:** Enter the function in the respective input field and choose the order of derivative

**Step 2:** Now click the button “Calculate” to get the derivative

**Step 3:** The derivative of the given function will be displayed in the new window

### What is the Derivative of a Function?

In calculus, one of the basic concepts is the derivative of a function. It occupies the central concept in calculus. We know that differentiation and integration are the two important concepts. Differentiation is the process of finding the derivative of a function, whereas integration is the process of finding the antiderivative of a function. The derivative of a function describes the rate of change. That means that it shows the amount by which the function is changing at the given point.

### Standard Form

The standard form to represent the derivative of a function is given below:

An infinitesimal change in the variable “x” is denoted by dx. Thus, the derivative of the variable “y” with respect to the variable “x” is given by **dy/dx**.

## Solved Examples on Derivatives

**Example 1:**

Find the first derivative of f(x) = 8x^{2} + 12x.

**Solution:**

Given function: f(x) = 8x^{2} + 12x.

Now, differentiating the function with respect of x, we get

(d/dx) (8x^{2} + 12x) = (d/dx) (8x^{2} ) + (d/dx)(12x)

(d/dx) (8x^{2} + 12x) = 16x + 12

Therefore, the first order derivative of the function 8x^{2} + 12x is 16x + 12.

**Example 2:**

Find the third derivative of f(x) = 14x^{4} – 2x.

**Solution:**

Given function: f(x) = 14x^{4} – 2x

Now, differentiate the function with respect to x, we get

First derivative:

(d/dx)(14x^{4} – 2x) = (d/dx)(14x^{4}) – (d/dx)(2x)

(d/dx)(14x^{4} – 2x) = 56x^{3} – 2

Second derivative:

(d^{2}/dx^{2})(14x^{4} – 2x) = 168x^{2} – 0

Third derivative:

(d^{3}/dx^{3})(14x^{4} – 2x) = 336x.

Therefore, the third derivative of f(x) = 14x^{4} – 2x is 336x.

**Example 3:**

Find the fifth derivative of f(x) = 6x^{7} + 5x^{3} – 2x.

**Solution:**

Given function: f(x) = 6x^{7} + 5x^{3} – 2x.

To find the derivatives of the given function, differentiate the function with respect to x.

First derivative:

(d/dx)(6x^{7} + 5x^{3} – 2x) = (d/dx)(6x^{7}) + (d/dx)(5x^{3}) – (d/dx)(2x)

(d/dx)(6x^{7} + 5x^{3} – 2x) = 42x^{6} + 15x^{2} – 2

Second derivative:

(d^{2}/dx^{2})(6x^{7} + 5x^{3} – 2x) = 252x^{5} + 30x – 0

Third derivative:

(d^{3}/dx^{3})(6x^{7} + 5x^{3} – 2x) = 1260x^{4} + 30

Fourth derivative:

(d^{4}/dx^{4})(6x^{7} + 5x^{3} – 2x) = 5040x^{3} + 0

Fifth Derivative:

(d^{5}/dx^{5})(6x^{7} + 5x^{3} – 2x) = 15120x^{2}

Hence, the fifth derivative of f(x) = 6x^{7} + 5x^{3} – 2x is 15120x^{2}.

**Also, check out:** Implict Differentiation Calculator.

## Frequently Asked Questions on The derivative calculator

### What is the derivative of zero?

In calculus, differentiation is the process of finding the derivative of a function. We know that the differentiation of any constant value is zero. Thus, the derivative of 0 is 0.

### What are the different methods to find the derivatives?

The different methods to find the derivative of a function are as follows:

- Calculating the derivative by definition
- Product Rule
- Chain Rule
- Implicit Differentiation
- Quotient Rule

### Define the first and second-order derivative.

Graphically, the first-order derivative defines the slope of the given function at a point. The second-order derivative explains how the slope changes over the independent variable for the given function.

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