What is a Derivative Rule?

A derivative rule in calculus is a formula or a set of rules that allows us to find the derivative of a function with respect to a given variable. The derivative of a function represents the rate at which the function changes with respect to that variable.

Basic Derivative Rules

There are several basic derivative rules that are commonly used to find derivatives quickly and efficiently:

• Power Rule: This rule is used to find the derivative of a power function. If f(x) = x^n, then f'(x) = nx^(n-1).
• Product Rule: This rule is used to find the derivative of a product of two functions. If f(x) = g(x) * h(x), then f'(x) = g'(x) * h(x) + g(x) * h'(x).
• Chain Rule: This rule is used to find the derivative of a composite function. If f(x) = g(h(x)), then f'(x) = g'(h(x)) * h'(x).

Applications of Derivative Rules

Derivative rules are essential in various fields such as physics, engineering, economics, and many more. They help us analyze the rate of change, optimize functions, determine critical points, and understand the behavior of functions.