What is the equation for derivatives

The derivative of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x. It is called "derivative" because it can be derived from the limit of the ratio of the change in y to the change in x as x changes.

The derivative is often written as:

dy/dx = f'(x)

or

df(x)/dx

where dy/dx signifies the derivative of the function f(x) with respect to x.

In more complex cases, the derivative can be calculated using various rules like the power rule, product rule, quotient rule, chain rule, etc.

For example, using the power rule (which states that the derivative of x^n, where n is any real number, is nx^(n-1)), the derivative of f(x) = x^2 would be f'(x) = 2x.