A 1st derivative is the rate of change of a function at a specific point. It describes how the function is changing at that point.
A 2nd derivative is the rate of change of the 1st derivative. It describes how the rate of change of the function is changing at a specific point.
The 1st derivative is important because it can tell us the direction and steepness of a function at a specific point. It can also help us find critical points, where the function changes from increasing to decreasing or vice versa.
The 1st derivative can be found using the power rule, product rule, quotient rule, or chain rule. The 2nd derivative can be found by taking the derivative of the 1st derivative.
The 2nd derivative is the rate of change of the 1st derivative, so it shows how the rate of change of the function is changing. A positive 2nd derivative indicates a concave up shape, while a negative 2nd derivative indicates a concave down shape. The 2nd derivative can also help us determine the inflection points of a function.