Second Order Derivatives (CIE A Level Maths: Pure 1)

What is the second order derivative of a function?

• If you differentiate the derivative of a function (ie differentiate the function a second time) you get the second order derivative of the function
• For a function y = f(x), there are two forms of notation for the second derivative (or second order derivative)

or 

• • Note the positions of the power of 2's in the second version 

• The second order derivative can also be referred to simply as the second derivative
  • Similarly, the 'regular' derivative can also be referred to as either the first order derivative or the first derivative
• The second order derivative gives the rate of change of the gradient function (ie of the first derivative) – this will be important for identifying the nature of stationary points