# Derivative Calculator

Derivative

## Definition of Derivative Calculator

The derivative of a function is a basic concept of mathematics. Derivative occupies a central place in calculus together with the integral. The process of solving the derivative is called differentiation & calculating integrals called integration.

Derivative Calculator is an latest addition of learning with technology. You can find the derivative of an inverse function calculator to solve your equations online and learn quickly.

## Trig Functions and Derivative Calculator

The rate of change of the function at some point characterizes as the derivative of trig functions. Derivative of inverse function calculator predict the rate of change by calculating the ratio of change of the function Y to the change of the independent variable X.

According to the definition of derivative, this ratio is considered in the limit as X approaches to 0 Δx→0.

## Leibniz Notation Calculator and Notations

In differentiation there is a significant role of Larange's notation and Leibniz notation. Leibniz notation calculator computes the results in view of those 2 notations.

In Lagrange's notation the derivative of f is written as function Y = f(x) as f′(x) or y′(x).

In Leibniz’s notation the derivative of f is written as function Y = f(x) as df / dx or dy / dx.

These are some steps to find the derivative of a function f(x) at the point x0 doing manual calculations:

• Form the difference quotient Δy/Δx = f(x0+Δx) −f(x0) / Δx
• If possible, Simplify the quotient, and cancel Δx
• First find the differentiation of f′(x0), applying the limit to the quotient. If this limit exists, then we can say that the function f(x) is differentiable at x0.

Derivatives of inverse functions calculator is an alternate to those manual calculations as derivative inverse calculator saves your time you spend doing manual calculations. It is used to increase the productivity and efficiency while learning.

Derivative also tells us the slope of a parabola at a given point. Therefore, it is said that first derivative is the slope of tanget line at a point which we calculate by using slope of a function calculator.

## The Derivative rules of differentiation calculator

Below is the list of all the derivative rules differentiate calculator uses:

## Constant Rule:

f(x) = C   then f ′(x) is equals to 0

The constant rule allows inverse derivative calculator to state the constant function of derivative is 0.

## Constant Multiple Rule:

g(x) = C * f(x) then g′(x) = c · f ′(x)

The constant multiple rule allows the derivatives of inverse functions calculator to make sure the constant of derivative is multiplied by the constant of derivative function.

## Difference and Sum Rule:

h(x) = f(x)±g(x) then h′(x) = f ′(x) ± g′(x)

The difference and sum rule will make sure the derivative of sum of function is the sum of their derivatives calculated by differentiation calculator.

## Product Rule:

h(x) = f(x)g(x) then h′(x) = f ′(x) g(x) + f(x) g′(x)

Product Rule allows the derivative of inverse calculator to multiply two parts of function together.

## Quotient Rule:

h(x) = f(x)/g(x) then, h′(x) = f ′(x) g(x) − f(x) g′(x)/g(x)²

Quotient rule allows differentiation calculator to divide one function with another.

## Chain Rule:

h(x) = f(g(x)) then h′(x) = f ′ (g(x)) g′(x)

The chain rule helps the differentiate calculator to differentiate the composite functions.

## Trigonometric Derivatives used by Differentiation Calculator

• Derivative of sinx f(x) = sin(x) then f ′(x) = cos(x)
• Derivative of cosx f(x) = cos(x) then f ′(x) = - sin(x)
• Derivative of tanx f(x) = tan(x) then f ′(x) = sec2(x)
• Derivative of secx f(x) = sec(x) then f ′(x) = sec(x) tan(x)
• Derivative of cotx f(x) = cot(x) then f ′(x) = - csc2(x)
• Derivative of cscx f(x) = csc(x) then f ′(x) = - csc(x) cot(x)

## Exponential Derivatives used by Differentiation Calculator

• f(x) = a˟  then; f ′(x) = ln(a)  a˟
• f(x) = e˟ then; f ′(x) = e˟
• f(x) = aᶢ˟ then    f ′(x) = ln(a)aᶢ˟ g′˟
• f(x) = eᶢ˟ then   f ′(x) = eᶢ˟ g′(x)

## Derivative of Sin

Sin(x) are the trigonometric function which play a big role in calculus.

The derivative of Sin is written as

$$\frac{d}{dx}[Sin(x)]=Cos(x)$$

## Derivative of Cos

Cos(x) is also an trignometric function which is as important as Sin(x) is.

The derivative of Cos is written as

$$\frac{d}{dx}[Cos(x)]=-Sin(x)$$

The derivative calculations are based on different formulas, find different derivative formulas on our portal.

## Derivative of Tan

There are more derivatives of tangent to find. In the general case, tan (x) where x is the function of tangent, such as tan g(x).

The derivative of Tan is written as

The derivative of tan(x) = sec2x.

## How to find the Derivative Calculator?

Derivative of inverse function calculator is an important tool for those who are seeking quick help regarding the calculations of derivative functions. It is not difficult to find the derivative calculator as you can easily search it online.

## What is Calculatored's Derivative Calculator?

Calculatored is an online platform offering tons of online tools and converters to students, teachers, reserachers and others. Derivative calculator is an equation simplifier which uses derivative quotient rule & derivative formula to find derivative of trig functions. Limits calculator and inverse Derivative calculator makes it easy to learn & solve equations.

## How to use Derivative Calculator?

The inverse function derivative calculator is simple, free and easy to use. This equation simplifier also simplifies derivative step by step.

Step #1: Search & Open differentiation calculator in our web portal.

Step #2: Enter your equation in the input field.

Step #3: Set differentiation variable as "x" or "y".

Step #4: Select how many times you want to differentiate.

Step #5: Click "CALCULATE" button.

Our inverse function calculator will quickly calculate the derivative of a function. You can find the derivative steps under the result.

We hope you liked our derivative calculator & its theory. Please provide us your feedback. Cheers!

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### Shaun Murphy

Last updated: September 09, 2020

I'm graduated in biomedical and electrical engineering. Specialization in sports and medical topics but will gladly tackle everything you throw at him. He is a sailor, hiker, and motorcyclist in his free time.