What is the derivative?

The derivative is a measure of the rate of change of f(x) as x varies. Alternatively it is the gradient of the tangent at a specific point of the graph. There are different rules for finding the derivative depending on the function we are given. For a polynomial, the derivative of x^n is n*x^(n-1), for sin(x) it is cos(x) and for cos(X) it is -sin(x). The derivative of e^x is e^x. It follows that the derivative of a constant value a is 0 since the rate of change is 0.