1. What Are Derivatives?

Derivatives represent the rate of change of a function with respect to its variable. The first derivative (f'(x)) measures instantaneous rate of change, the second derivative (f''(x)) measures the rate of change of the first derivative, and the third derivative (f'''(x)) measures the rate of change of the second derivative.

2. How Derivative Calculation Works

Derivatives are calculated using the limit definition:

Higher-order derivatives are found by repeatedly applying the differentiation process:

• 2nd derivative: derivative of the first derivative
• 3rd derivative: derivative of the second derivative

3. Applications of Derivatives

Details: Derivatives are fundamental in physics (velocity, acceleration), engineering (optimization), economics (marginal analysis), and many other fields where rate of change is important.

4. Using the Calculator

Tips: Enter a mathematical function using standard notation (e.g., x^2, sin(x), exp(x)), specify the point where you want to calculate the derivative, and select the derivative order (1st, 2nd, or 3rd).

5. Frequently Asked Questions (FAQ)

Q1: What functions can I input?
A: The calculator supports basic mathematical functions including polynomials, trigonometric functions, exponential functions, and logarithms.

Q2: How accurate are the results?
A: The calculator uses symbolic differentiation for precise results, not numerical approximation.

Q3: Can I calculate partial derivatives?
A: This calculator is designed for ordinary derivatives. For partial derivatives, use a specialized multivariable calculator.

Q4: What if my function is not differentiable at the point?
A: The calculator will return an error or undefined result for points where the derivative does not exist.

Q5: Can I save my calculations?
A: Currently, the calculator does not have a save feature. You can manually record your inputs and results.