1. MTH1170 Higher Order Derivatives

2. Preliminary
If the derivative y’ = f’(x) of a function y = f(x) is itself differentiable at x, we can calculate its derivative, which we call the second derivative of f. This new function is denoted by y” = f"(x).

3. Notation
Second derivatives can be represented using the following notation:

4. Higher Order Derivatives
After we have calculated the second derivative, we can move on to the third, fourth, and in general the nth order derivatives.

5. Velocity and Acceleration
One application for using higher order derivatives is with velocity and acceleration. If we are given an objects position as a function of time, we can find it’s velocity and acceleration by taking the first and second derivatives respectively.

6. Velocity and Acceleration

7. Example

8. Example

9. Example