Introduction of derivative calculator with steps

Calculus is a branch of mathematics that deals with two major concepts: integration and differentiation. Differentiation is the process of finding the rate of change of a function with respect to its input variable. It is the inverse of integration, which is the process of finding the area under a curve.

The calculation of derivatives can be technical and requires proper consideration and focus. Fortunately, the derivative calculator is an online tool that provides a complete solution for differentiation. The differentiate calculator with steps helps users calculate derivatives quickly and easily with just a few clicks.

The online derivative calculator provides useful results in the form of steps, which helps users and specifically students to learn this concept in detail. The step-by-step solutions provided by the derivative calculator can also help users understand the rules and formulas used in differentiation.

Besides differentiation calculator, there are other tools such as second derivative calculator, third derivative calculator, implicit differentiation calculator and many more.

By using the derivative calculator and other related tools and resources available on our website, users can gain a deeper understanding of calculus and how it is used in real-world applications. So, whether you are a student, a professional, or just someone interested in mathematics, our website has something to offer you.

To make the most of our website and its tools, we encourage you to explore all of the resources available and learn as much as you can about calculus and differentiation.

Formulas used by online derivative calculator

The derivative 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 $

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:

$ \frac{d}{dx} (f(x) \pm g(x)) = \frac{d}{dx}f(x) \pm \frac{d}{dx}g(x) $

• 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

• 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) $

• 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} $

How does a derivative calculator work?

The derivative calculator is an online tool that uses derivative formulas and rules to compute accurate results. The tool lets users provide input in the form of an equation, which can be entered using a variety of formats, including standard algebraic notation, function notation, or even graphical representations.

Once the equation is entered, the derivative calculator applies different derivative rules or formulas to solve it and compute the derivative. These rules and formulas can include the power rule, the product rule, the quotient rule, and many others.

The derivative calculator also provides step-by-step solutions that can help users understand the process behind the calculation of derivatives. This can be particularly useful for students who are learning calculus and need to practice solving problems and understanding the rules and formulas used in differentiation.

Overall, the derivative calculator is an easy-to-use and efficient tool that can help you calculate derivatives quickly and accurately. By using this tool, you can save time and focus on understanding the concepts behind differentiation, rather than spending hours calculating derivatives by hand.

How to find a derivative calculator with steps?

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.

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.

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 differentiate this simple function manually. Moreover, we may also 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 derivative 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 trigonometric function which is somehow complex for students that cannot remember trigonometric 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.