Polynomial Derivative Calculator

How to calculate a derivative?

The most fundamental rule for finding a derivative is the Power Rule. This rule is used when a variable is raised to a fixed power, allowing you to quickly determine the rate of change for polynomial functions.

d/dx [ax^n] = anx^(n-1)

Using the Derivative Calculator: an example

Suppose you want to find the derivative of the function f(x) = 5x³. In this case, our coefficient 'a' is 5 and our exponent 'n' is 3.

Step-by-step calculation:

1. Multiplication: Multiply the coefficient (5) by the original exponent (3) to get 15.
2. Subtraction: Subtract 1 from the original exponent (3 - 1) to get the new exponent of 2.

By following these steps, the derivative of 5x³ is 15x².

Frequently Asked Questions

What is a derivative?
A derivative is a tool in calculus that measures the instantaneous rate at which a function changes at any specific point.

What is the derivative of a constant?
The derivative of any constant number (like 7 or 42) is always zero because constants do not change.

Does this work for negative exponents?
Yes, the power rule works for all real numbers, including negative integers and fractional exponents.