# Derivative Calculator

## Definition of Derivative Calculator with steps

In calculus, there are two major concepts i.e. integration and differentiation. Differentiation is the inverse of integration. Like integration, calculation of derivatives are technical and requires proper consideration and focus.

Derivative calculator is an online tool which provides a complete solution of differentiation. The differentiation calculator helps someone to calculate derivatives on run time with few clicks.

Differentiate calculator provides useful results in the form of steps which helps users and specifically the students to learn this concept in detail.

For calculating derivatives in term of x and y, use implicit differentiation calculator with steps.

## Formulas used by Derivative Calculator

The derivatives of inverse functions calculator uses the below mentioned formula to find derivatives of a function. The derivative formula is:

$$\frac{dy}{dx} = \lim\limits_{Δx \to 0} \frac{f(x+Δx) - f(x)}{Δx}$$

Apart from the standard derivative formula, there are many other formulas through which you can find derivatives of a function. These calculations formulas are:

$$\frac{d}{dx}(Sin x) = Cos x$$ $$\frac{d}{dx}(Cos x) = -Sin x$$ $$\frac{d}{dx}(tan x) = Sec^2 x$$ $$\frac{d}{dx}(Csx x) = -Csc x Cot x$$ $$\frac{d}{dx}(Sec x) = Sec x Tan x$$ $$\frac{d}{dx}(Cot x) = -Csc^2 x$$

Related: Click on calculus, if you want to learn different ways of finding derivative of a function.

## Derivative rules used by Differentiation Calculator

With derivative, we can find the slope of a function at any given point. The differentiation rules are used for computing the derivative of a function. The most important differentiation rules are:

• Derivative of Constant:
• $$\frac{d}{dx}(constant) = 0$$
• Power Rule:
• $$\frac{d}{dx}(x^n)=n x^{n-1}$$
• Constant Multiple Rule:
• $$\frac{d}{dx}[cf(x)] = c. \frac{d}{dx}f(x)$$

Here, c = Real number

• Sum and Difference Rule:
• $$\frac{d}{dx} (f(x) \pm g(x)) = \frac{d}{dx}f(x) \pm \frac{d}{dx}g(x)$$

• Product rule:
• $$\frac{d}{dx}[f(x) \cdot g(x)] = f(x) \frac{d}{dx}[g(x)] + g(x) \frac{d}{dx}[f(x)]$$

or

$$\frac{d}{dx}[f(x) \cdot g(x)] = f(x)g'(x) + g(x)f'(x)$$

You can also use product rule derivative calculator for learning and practice.

• Quotient Rule:
• $$\frac{d}{dx} \left[ \frac{f(x)}{g(x)} \right] = \frac{g(x)\frac{d}{dx}[f(x)]−f(x) \frac{d}{dx}[g(x)]}{[g(x)]^2}$$

Also find quotient rule derivative calculator for more precise calculations.

This website provides a complete solution to differentiation and all the calculations regarding derivatives. Find partial differentiation calculator and directional derivative calculator on this website to further strengthen your concepts regarding differentiation.

## How does a Derivative Calculator work?

Derivative calculator with steps is an online tool which uses derivative formulas and rules to compute accurate results. The differentiate calculator lets users provide input in the form of an equation.

The differentiate calculator then solves that equation while using different derivative rules or formulas. If you further want to calculate, use second derivative calculator with steps.

Furthermore, if you want to calculate it more higher, this website has another solution for you. You can use the third derivative calculator with steps on this platform for you having accurate results.

## How to find Derivative Calculator?

It is not difficult to find an online derivative calculator. You can either type the full url of this differentiation calculator on your search engine or you can search on Google with its name. You can search on google with "derivative calculator" or "inverse derivative calculator" and you'll find our latest and accurate online tool.

Related: On this platform, you can also find tangent line approximation using linearization calculator. You can also get a lot of help from using chain rule derivative calculator free online.

## How to use Derivative Calculator with steps?

Our differentiate calculator is very easy to operate as you need to follow the below mentioned procedure as:

1. Write your equation in the first input or load any equation by clicking on the button.
2. Select the variable you want to differentiate.
3. Select how many times you want to differentiate.
4. Click on the “CALCULATE” button.

Immediately after clicking on the calculate button, our differentiation calculator will solve your equation and provide detailed results. These results help you understand and learn the concept by practicing on run time.

For consolidating you calculations regarding to the normal line of the equation, you need to try equation of normal line calculator offered by this websites.

## Related Calculators

There are a lot of other related calculators to differential calculator which you can use on this website for free. These tools are:

## Frequently Asked Questions

### How to differentiate the function f(x)=5.4x+2.4?

Given function is:

$$f(x) \;=\; 5.4x+2.4$$

Differentiating on both sides with respect to ‘x’

$$f'(x) \;=\; d/dx(5.4x+2.4)$$

We have,

$$f'(x) \;=\; d/dx(5.4x)+d/dx(2.4)$$ $$f'(x) \;=\; 5.4(1)+0 \;=\; 5.4$$

In this way, we may differentite this simple function manually. Moreover, we may also use differentiate the function calculator for online calculations.

### How to calculate the derivative of a function?

To calculate derivative of a function, you have to perform following steps:

1. Remember that a derivative is the calculation of rate of change of a function.
2. Apply the derivative on the function with respect to independent variable involved in the function.
3. Simplify the function to get exact value of derivative.

The same procedure has been used by derivatives calculator to calculate the rate of change of function online.

### What is the Derivative of x?

The derivatve of x is 1. It refers of the result that is produced by differentiating x in different ways. Finding a function's rate of change involves the process of differentiation. Thus you can find the derivative calculator for this process.

### What is the derivative of cos2(x)?

The derivative of cos2(x) is,

$$\frac{d}{dx} (cos^2⁡x) \;=\; -2 cos⁡(x) \cdot sin(⁡x) \;=\; -sin^⁡2x$$

The derivative of cos2x is the the derivative of trignometric function which is somehow complex for students that cannot remember trignometric identities. For such students, derivative solver is the great tool for calculating derivative of a trigonometric function.

### How to differentiate ex?

Since the derivative of an exponential function with base "e" equals ex, the differentiation of e to the power x is equivalent to e to the power x itself. It is written mathematically as d/dx (ex) = ex.

This may evaluate in differentiation solver for cross verification of answer and its steps online.

### Alan Walker

Last Updated November 21, 2022

I am Mathematician, Tech geek and a content writer. I love solving patterns of different math queries and write in a way that anyone can understand. Math and Technology has done its part and now its the time for us to get benefits from it.