How can I visualize derivatives in calculus?

How can I visualize derivatives in calculus?

You can visualize derivatives using graphs. The derivative represents the slope of the tangent line at any point on a curve.

Can you show me an example with a specific function?

Sure! Let's take the function f(x) = x^2. The derivative, f'(x) = 2x, gives the slope of the tangent line at any point.

How do I graph the derivative?

To graph the derivative, plot the function f'(x) = 2x. For example, at x=1, the slope is 2, so the tangent line at (1,1) will rise steeply.

What tools can I use to visualize these graphs?

You can use graphing calculators, software like Desmos, or programming languages like Python with libraries such as Matplotlib.