What Are Derivatives?

If you are talking about derivatives of graphs, they are plots of slopes at different points of a graph.

For example, consider the graph of y=x. When x=3, y=3. At this point, the slope equals 1. x=5, y=5, the slope equals 1 again. Take as many x/y values, and you will see that the derivative of the y=x graph is simply y=1 (horizontal line crossing y-axis at 1).

This is a simple example. To find the derivative of more complex graphs, basic calculus might be simpler

The power rule says that to find the derivative graph of an original graph, you can take an equation's power, multiply it by that power, and then subtract 1 from that power.

Consider the graph of the parabola y=x^2. Using the power rule, we multiply by the power (2) to get y=2x^2, then we subtract 1 from the power to get y=2x^1 or simply y=2x. So y=2x is the derivative graph of the equation y=x^2. To find the derivative of a point on y=x^2, simply plug the x value into the derivative. Take the point x=2 so y=2(2) =4. So at the point x=2 on the graph y=x^2, the derivative (slope) is 4.

In summary, the derivative of a point on a graph is simply its rate of change, graphically known as its slope.

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