Higher Order Derivatives

• First order derivative: f'(x) or dy/dx, also called "First Derivative"

• Second order derivative: f''(x) or d²y/dx², also called "Second Derivative"

• ...

Second derivatives

The second derivative of a function is simply the derivative of the function's derivative.

Notation: Leibniz's notation for second derivative is:

Second derivatives of implicit equations

▶ Back to previous note on Implicit Differentiation ▶ Practice at Khan academy: Second derivatives (implicit equations)

▶ Online calculator for 2nd Derivative of Implicit equations

Example

Solve:

Example

Solve:

• The first derivative is:

  
• The second derivative is:

  
• Plug in y=1, and get: