**Derivative Formula**

Small Description: Meta-description: In the world of Mathematics, the derivative formula helps in determining the slope of any line.

A derivative is a tool that allows us to see how the connection between two variables changes over time. For understanding purposes, take the independent variable ‘x’ and the dependent variable ‘y’ as examples. So, the derivative formula can be used to calculate the change in the value of the ‘y’ in relation to the change in the value of the independent variable ‘x’ expression. The derivative formula is used in mathematics for determining the slope of a line, the slope of a curve, and the change in one measurement with respect to some other measurement.

**Basic formula**

The derivative formula is considered to be one of the most fundamental notions in calculus, and differentiation is the process of determining a derivative. For a variable ‘x’ with an exponent of ‘n,’ the formula is defined. The exponent ‘n’ can be a rational fraction of an integer. As a result, the derivative is always calculated using the following basic and universally accepted formula:

**Derivative Formula Rules**

There are seven basic types of rules that are commonly used to address problems with derivatives:

1. The Power rule

Mathematically it is expressed as:

2. Product Rule

When there is involvement of two functions a(x) and b(x) then their product f(x) is given as below:

3. Quotient Rule

4. Sum or Difference rule: The sum/difference formula asserts that when any function f(x) is the sum or the difference of the given two functions a(x) and b(x), then it is stated as:

5. Derivative of a constant: it is always zero for any constant c.

6. Derivative of a constant multiplied by a function

7. Chain Rule

**Some Important Formulas**

A few additional essential derivation formulas used in various branches of mathematics, such as calculus and trigonometry, are listed below. Differentiate values of trigonometric functions are done with the use of the derivative formulas mentioned below.

1) Trigonometric functions

**Solved Examples**