The derivative of a function represents the limiting value of the ratio of the change in that function to the corresponding change in its independent variable. This describes the instantaneous rate of change of a function with respect to a variable. In practical terms the derivative of a function represents the slope of the graph of that equation at a given point. The derivative of a function f(x) is defined mathematically as: f'(x) = lim_h0 (f(x + h) - f(x))/h, where h is a defined interval on x. The differential of a function f(x) is the derivative of that function with respect to x multiplied by the increment interval, usually denoted as dx. df = f'(x)dx, where df is the differential of f at x with increment dx. From this equation, along with the fact that dx = h...