Derivative Formula

A derivative helps us to know the changing relationship between two variables. Consider the independent variable ‘x’ and the dependent variable ‘y’. The change in the value of the dependent variable with respect to the change in the value of the independent variable expression can be found using the derivative formula. Mathematically, the derivative formula is helpful to find the slope of a line, to find the slope of a curve, and to find the change in one measurement with respect to another measurement. In this section, we will learn more about the derivative formula and solve a few examples.

What is Derivative Formula?

The derivative formula is one of the basic concepts used in calculus and the process of finding a derivative is known as differentiation. The derivative formula is defined for a variable ‘x’ having an exponent ‘n’. The exponent ‘n’ can be an integer or a rational fraction. Hence, the formula to calculate the derivative is:

Rules of Derivative Formula

There are some basic derivative formulas i.e. a set of derivative formulas that are used at different levels and aspects. The below image has the rules.

Derivation of Derivative Formula

Let f(x) is a function whose domain contains an open interval about some point x0x0. Then the function f(x) is said to be differentiable at point (x)0(x)0, and the derivative of f(x) at (x)0(x)0 is represented using formula as:

f'(x)= lim_Δx→0 Δy/Δx

⇒ f'(x)= lim_Δx→0 [f((x)0(x)0+Δx)−f((x)0(x)0)]/Δx

Derivative of the function y = f(x) can be denoted as f′(x) or y′(x).

Also, Leibniz’s notation is popular to write the derivative of the function y = f(x) as df(x)/dx i.e. dy/dx

List of Derivative Formulas

Listed below are a few more important derivative formulas used in different fields of mathematics like calculus, trigonometry, etc. The differentiation of Trigonometric functions uses various derivative formulas listed here. All the derivative formulas are derived from the differentiation of the first principle.

Derivative Formulas of Elementary Functions

Derivative Formulas of Trigonometric Functions

Derivative Formulas of Hyperbolic Functions

Differentiation of Inverse Trigonometric Functions

Differentiation of Inverse Hyperbolic Functions

Examples Using Derivative Formula

Example 1: Find the derivative of x⁷ using the derivative formula.

Solution:

FAQs on Derivative Formula

What is Meant by Derivative Formula?

Derivative formula is one of the fundamental aspects used in calculus. The dervative function measures sensivity of a variable which is calculated by using a quantity. A derivative helps us to know the changing relationship between two variables. Mathematically, the derivative formula is helpful to find the slope of a line, to find the slope of a curve, and to find the change in one measurement with respect to another measurement. The

What are the Basic Rules of Derivative Formula?

The basic rules of derivative formulas are:

• Constant Rule
• Constant Multiple Rule
• Power Rule
• Sum Rule
• Difference Rule
• Product Rule (UV differentiation formula)
• Chain Rule
• Quotient Rule

What is The Derivative of f(x) = 25 ?

Since the function f(x) is constant, according to the derivative formula, its derivative will be zero i.e. f’(x) = 0

Definition of The Derivative

Chain Rule

The last formula

Higher Derivative Formula for the Product: Leibniz Formula

Introduction to Derivatives

Let us Find a Derivative!

To find the derivative of a function y = f(x) we use the slope formula:

Let’s try another example.

Result: the derivative of x³ is 3x²

Derivative Formula

Derivatives are a fundamental tool of calculus. The derivative of a function of a real variable measures the sensitivity to change of a quantity, which is determined by another quantity.Derivative Formula is given as,

Differentiation Formulas PDF

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