## Definition of Derivative

As per the definition of derivative, Let f(x) be a function whose domain consist on an open interval at some point x0. Then the function f(x)is known to be a differentiable at x0, and the derivative of f(x) at x0 is given by

f′(x0) =limΔx→0Δy/Δx=limΔx→0; f(x0+Δx) −f(x0) / Δx

## What is Derivative?

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 & solving integrals called integration.

## Derivative of Trig Functions

The rate of change of the function at some point characterizes as the derivative of trig functions. We can 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.

Derivative of trig functions also help to learn quadratic formula & standard deviation.

## Lagrange's Notation

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

## Leibniz's Notation

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:

- 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.

## The Derivative rules

A list of all the derivative rules differential calculator uses:

## Constant Rule:

f(x) = C then f ′(x) is equals to 0

## Constant Multiple Rule:

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

## Difference and Sum Rule:

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

## Product Rule:

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

## Quotient Rule:

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

## Chain Rule:

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

For general calculations involving area, find trapezoid area calculator along with area of a sector calculator & rectangle area calculator.

## Trigonometric Derivatives

- 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)

Click on to learn the calculations of arithmetic sequence & pythagorean theorem.

## Exponential Derivatives

- 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

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

## 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.

## What is Derivative Calculator?

Our derivative calculator is an equation simplifier which uses derivative quotient rule & derivative formula to find derivative of trig functions. Partial Derivative calculator makes it easy to learn & solve equations.

## How to use Derivative Calculator?

Our derivative calculator is very easy to use. This equation simplifier also simplifies derivative step by step.

You have to enter equation, like cos (2x)

After you entered the equation then press "CALCULATE" button and the derivative of the function is calculated by inverse function calculator.

That is how easy it is to use our partial derivative calculator. You can also find steps of your equation below in the result section of our implicit differentiation calculator.

You can also use our other math related calculators like summation calculator or gcf calculator.

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