1. What is Third Order Derivative?

The third order derivative, denoted as \(\frac{d^3y}{dx^3}\), represents the rate of change of the second derivative of a function. It provides information about the jerk or the rate of change of acceleration in physical applications.

2. How Does the Calculator Work?

The calculator computes the third derivative of the input function using symbolic differentiation techniques:

Where:

• \( y \) — Input function of x
• \( \frac{d^2y}{dx^2} \) — Second derivative of y with respect to x
• \( \frac{d}{dx} \) — Differentiation operator

Explanation: The calculator applies differentiation rules (power rule, product rule, chain rule, etc.) three times to compute the third order derivative.

3. Importance of Third Order Derivatives

Details: Third order derivatives are important in physics for analyzing jerk in motion, in engineering for studying vibration systems, and in economics for understanding rate of change of acceleration in economic models.

4. Using the Calculator

Tips: Enter a mathematical function of x using standard notation (e.g., x^2, sin(x), exp(x)). Ensure the function is differentiable to the third order.

5. Frequently Asked Questions (FAQ)

Q1: What types of functions can be differentiated?
A: The calculator can handle polynomial, trigonometric, exponential, logarithmic, and other standard mathematical functions.

Q2: How accurate are the results?
A: Results are symbolically computed and mathematically exact for valid input functions.

Q3: Can I use variables other than x?
A: The calculator currently only supports functions of x as the independent variable.

Q4: What if my function is not differentiable?
A: The calculator will return an error or undefined result for functions that are not differentiable to the third order.

Q5: Can I calculate higher order derivatives?
A: This calculator specifically computes third order derivatives. For other orders, use the appropriate derivative calculator.