What are derivatives in calculus?

What are derivatives in calculus?

Derivatives represent the rate of change of a function. They measure how a function's output changes as its input changes.

Can you give me an example of how to calculate a derivative?

Sure! For the function f(x) = x^2, the derivative f'(x) = 2x. This means for every unit increase in x, f(x) increases by 2x.

What does the derivative tell us about the graph of a function?

The derivative indicates the slope of the tangent line to the graph at any point, showing whether the function is increasing or decreasing.

Are there different rules for finding derivatives?

Yes, there are several rules like the power rule, product rule, and quotient rule that help in finding derivatives of various functions.