What does the derivative mean in simple terms?

Problem Statement

What does the derivative mean in simple terms?

Step-by-Step Explanation

A derivative is the slope of a curve at a point and tells how fast a quantity is changing.

1. Identify what the question is asking. In Calculus, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
3. Work one step at a time and keep units, signs, and restrictions visible.
4. Check whether the answer makes sense in the original context.

Final Answer

A derivative is the slope of a curve at a point and tells how fast a quantity is changing. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.