Differentiation of Composite & Inverse Functions

#Table of Contents

1. Second Derivatives
   • What is a second derivative?
   • Worked Example
2. Higher-Order Derivatives
   • What are higher-order derivatives?
   • Worked Example
3. Practice Questions
4. Glossary
5. Summary and Key Takeaways

#Second Derivatives

#What is a second derivative?

The second derivative of a function is the derivative of the derivative. It measures the rate of change of the rate of change of a function.

Key Points:

• The second derivative is denoted as:
  • $$f''(x)$$
  • $$\frac{d^2 y}{dx^2}$$
  • $$y''$$
• The second derivative helps in understanding the concavity of a function's graph.

To find the second derivative, differentiate the function and then differentiate the result once more. Both the function and its first derivative must be differentiable for this to work.

#Worked Example

A function $f$ is defined by $f(x) = 3x^3 - 2x^2 - 3x + 2$. Find the second derivative of $f(x)$.

Solution: ...