# Are You Ready to Solve First and Higher – Order Derivatives

Are You Ready to Solve First And Higher – Calculus deals with differentiation which is the process of finding the rate of change of a function with its variables. Our derivative calculator is the best and quick way to find out the changing functions with their variables.

It provides useful results which help users, especially students and teachers to solve the derivatives within a few seconds and get fast step-by-step calculations.

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## What Are Derivatives?

In Mathematics;

It is the fundamental concept of calculus that means how the function changes as the input values or variables change. Derivatives mean finding out the slope of the giving function. It means that it is the rate of change of the function as the variables change we say that as the functions change.

As we already know, the formula of derivatives is helpful to solve the first and higher-order derivatives as well as with the different functions. Let’s take a quick look at the formula below to repeat the concept.

## Derivative Formula:

Derivatives are the specific way to find the tangent line that is drawn in the graph at a specific point. This scenario is used to find the equation. It also is used to find the maximum and the minimum values of the function. For which equation, these tactics use the below equation.

f'(x) = lim(h -> 0) [(f(x + h) – f(x)) / h]

Our derivative calculator is a unique way to solve and clarify these types of queries by just putting the values in the field. But if your goal comes up with manual calculations, you may use the above-given formula for the function of variables:

## Basic Functions of Derivatives

How many types of derivatives or how many basic functions? All search for this query so our online derivative calculator will make it easy for you. There are the following functions of the derivatives. See all with their basic formulas;

• Derivation of sin x: (sin x)’ = cos x.
• Derivative of cos x: (cos x)’ = -sin x.
• Derivative of tan x: (tan x)’ = sec2 x.
• Derivative of cot x: (cot x)’ = -cosec 2x.
• Derivative of sec x: (sec x)’ = sec x. tan x.
• Derivative of cosec x: (cosec x)’ = -cosec x. cot x.

## Rules of derivatives

With the help of derivatives, you can find out the slope of the function for any point by just putting the values. There are some differentiation rules to find the derivations. These rules will prove helpful in finding the changing functions as well as their variables. Rules are given below;

• Derivative of constant
• Power rule
• Constant multiple rules
• Product rule

## Derivative of constant

The derivative of the constant is the rule of changing function. According to this rule, all constant functions must be equal to zero.

d/dx(constant) = 0

## Power Rule

The power rule is d d x (a x n) = n an x n 1 for the derivative of a power function. To put it simply, reducing the exponent value down, multiplying it by the function, and then deducting one from the exponent are the steps involved in calculating the derivative of a power function.

d/dx(x^n)=n x^{n-1}

## Constant multiple rules

According to this one, constant derivatives are equal to the constant functions derivatives. According to the Constant Rule, any constant function’s derivative is always equal to zero.

d/dx[cf(x)] = c.d/dx{f(x)}

## Product rule

According to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the derivative of the second function plus 2nd function with the derivative of the first function. When taking the derivative of the quotient of two functions, one must use the Product Rule.

d/dx[f(x) .g(x)] = f(x)g'(x) + g(x)f'(x)

## Final Words:

With the help of our free derivative tool, you can find the derivative of any function with its variables. The derivative calculator is one of the main tools in calculus. It is the rate of change of a function and this is the same as the slope of a tangent line that is drawn to the graph of a function.