Are you a student, teacher, or professional needing quick derivative calculations? Our Derive Calculator is the perfect online tool to help you calculate the first to fifth-order derivatives of any mathematical function. Whether you’re dealing with polynomials, trigonometric expressions, or exponential/logarithmic equations, this calculator simplifies your work with instant results and optional value evaluations.
Derive Calculator
Function Input
Evaluation (Optional)
Original Function:
f(x) =Derivative:
f'(x) =Function Syntax Guide:
- Addition: x + 2
- Subtraction: x – 2
- Multiplication: x * 2
- Division: x / 2
- Exponents: x^2 or x**2
- Sine: sin(x)
- Cosine: cos(x)
- Exponential: exp(x)
- Natural Log: ln(x)
- Parentheses: (x + 1)^2
🧮 What Is a Derive Calculator?
A Derive Calculator is a digital tool designed to compute the derivative of a function with respect to a variable. It supports up to the fifth-order derivative and allows you to evaluate the derivative at any specific value of the variable.
This tool is useful in fields such as:
- Mathematics
- Engineering
- Physics
- Economics
- Computer Science
✅ Key Features
- Supports first to fifth-order derivatives
- Customizable variable input
- Optional evaluation at specific points
- Intuitive design for both beginners and experts
- Supports complex functions like
sin(x),ln(x),exp(x), etc.
🧑🏫 How to Use the Derive Calculator
Follow these steps:
1. Enter the Function
In the field labeled “Enter Function f(x):”, input the expression. Examples:
x^2 + 3x + 2sin(x) + x^3ln(x) * exp(x)
2. Set the Variable
By default, the variable is set to x. You can change it to any single character (e.g., t, y, etc.) if needed.
3. Choose Derivative Order
Select between:
- First (
f') - Second (
f'') - Third (
f''') - Fourth (
f⁽⁴⁾) - Fifth (
f⁽⁵⁾)
4. Evaluate at a Point (Optional)
Want to find the numerical value of the derivative at a specific point? Input a number in the “Evaluate at x =” field.
5. Click “Calculate”
Results will instantly appear:
- The original function
- The calculated derivative
- The evaluation result (if a point was entered)
6. Click “Reset” to clear all inputs and results.
📘 Example Calculations
Example 1: First Derivative of x^2 + 3x + 2
Input:
- Function:
x^2 + 3x + 2 - Variable:
x - Derivative Order:
1
Result:
f(x) = x^2 + 3x + 2
f'(x) = 2x + 3
Example 2: Second Derivative of sin(x)
Input:
- Function:
sin(x) - Variable:
x - Derivative Order:
2
Result:
f(x) = sin(x)
f''(x) = -sin(x)
Example 3: Evaluate Third Derivative of x^4 at x = 2
Input:
- Function:
x^4 - Order:
3 - Evaluate at x =
2
Result:
f(x) = x^4
f'''(x) = 24x
f'''(2) = 48
📌 Supported Function Syntax
Make sure your input follows these formats:
| Operation | Syntax Example |
|---|---|
| Addition | x + 2 |
| Subtraction | x - 3 |
| Multiplication | x * 4 |
| Division | x / 5 |
| Power/Exponent | x^2 or x**2 |
| Sine | sin(x) |
| Cosine | cos(x) |
| Logarithm (ln) | ln(x) |
| Exponential | exp(x) |
| Parentheses | (x + 2)^2 |
❓ 20 Frequently Asked Questions (FAQs)
1. What is the derivative of a function?
The derivative represents the rate at which a function changes. It is the slope of the tangent line at any point.
2. Can I calculate higher-order derivatives?
Yes, the calculator supports up to the fifth-order derivative.
3. What does ‘f′(x)’ mean?
It represents the first derivative of a function f with respect to x.
4. Can I evaluate the derivative at a specific point?
Yes. Enter a number in the “Evaluate at x =” field.
5. Does it support functions like sin(x) and ln(x)?
Absolutely. It supports trigonometric, logarithmic, and exponential functions.
6. Is it case-sensitive?
Yes, use lowercase variable names (x, t, y, etc.).
7. What if I enter invalid syntax?
You will receive an alert prompting you to correct your input.
8. Can I use parentheses?
Yes, use parentheses for grouping operations, like (x + 1)^2.
9. Is the tool mobile-friendly?
Yes, the design is responsive and works on mobile, tablet, and desktop devices.
10. Is it free to use?
Yes, it's completely free and accessible online.
11. How does it calculate derivatives?
It uses the math.js library to symbolically differentiate functions.
12. Can I change the variable name?
Yes, you can use any single character like x, y, t, etc.
13. Can I input complex expressions?
Yes, as long as the syntax is correct.
14. Is there a limit to function length?
There is no strict limit, but keep functions manageable for accurate parsing.
15. Is it accurate for school or university use?
Yes, it uses reliable mathematical libraries suitable for academic use.
16. Can I use x**2 instead of x^2?
Yes, both are supported.
17. Does it simplify the derivative automatically?
Yes, the output is a simplified derivative expression.
18. Can I see steps or just results?
Currently, only the final result is shown.
19. What happens when I click reset?
It clears all inputs and results to let you start fresh.
20. Do I need an internet connection?
Yes, it’s a web-based tool and requires internet access.
🔚 Final Thoughts
Whether you're checking homework, analyzing equations, or preparing reports, the Derive Calculator makes derivative computations fast and effortless. With a clean design and powerful math capabilities, it’s perfect for learners and professionals alike.