Say you have a graph with an equation like this:
You can differentiate this equation using the below formula.
In this equation, n is 2, so to differentiate this equation, the number 2 has to be before the x and the power has to be subtracted by 1. So we will get this equation:
means the derivative of y with respect to x.
Differentiating a graph can allow you to find the gradient of a tangent at a certain point. If you replace the x with the x-coordinate of the point in the differentiated equation, you can find the gradient. For example, if we wanted to find the tangent of a graph where x was equal to 2, we would have to substitute 2 for x.
Here the gradient of the tangent at x = 2 is 4.
If you have an equation where different terms of x are added or subtracted, you differentiate each term separately. For example,
You can see how each separate term has been differentiated in this example.