Higher order derivatives are derivatives that are taken multiple times on a function. For example given the function the first 3 derivatives take the form

• First Derivative -
• Second Derivative -
• Third Derivative -

Notation

There are 2 main notations for the higher order derivatives each of which have their own strengths

• Leibniz's Notation
• Lagrange's Notation

Meanings

Meaning of the Second Derivative

The second derivative can be though of as the rate at which the derivative of a function changes at a given point.

This second derivative also represents the concavity of a given graph at a point. Locations where the second derivative switches signs (ie. from or from ) represent a spot where the original graph has an inflection point.