Derivative Calculator
What Is a Derivative?
In calculus, a derivative measures how a function changes as its input changes. In simpler terms, it tells you the rate of change or slope of a curve at any given point.
For example:
- The derivative of
x²is2x, which shows how the value ofx²changes asxincreases or decreases. - In real life, derivatives are used to calculate things like velocity, acceleration, growth rates, and margins.
How This Derivative Calculator Works
Our online derivative calculator is powered by Math.js and MathJax to give you accurate results with LaTeX-style math rendering.
Here’s how it works:
- Enter a function of
x(e.g.sin(x),x^3 + 2x, orsqrt(x^2 + 1)). - Use the math buttons to insert symbols like
π,√,e,sin,cos, and more. - Click Go! to instantly calculate the derivative.
- The result will appear in a nicely formatted math output using MathJax.
You can also see a live preview of your function before you calculate it.
Key Features
- ✅ Instant Derivative Results
- ✅ Supports Trigonometric, Logarithmic, and Exponential Functions
- ✅ Clean Math Output with LaTeX Formatting
- ✅ Easy-to-use Math Buttons
- ✅ Fully Responsive (Mobile + Desktop)
- ✅ No Signup Required — 100% Free
Example Calculations
| Input Function | Derivative |
|---|---|
x^2 + 3x + 2 | 2x + 3 |
sin(x) | cos(x) |
sqrt(x^2 + 1) | x / sqrt(x^2 + 1) |
ln(x) | 1 / x |
e^(2x) | 2e^(2x) |
What Are Derivatives Used For?
Derivatives are used in many real-world applications:
- 📈 Economics – to find marginal cost and revenue
- 🚗 Physics – to calculate velocity, acceleration
- 💹 Finance – for rate of return and modeling curves
- 🧠 Machine Learning – for optimizing algorithms via gradients
- 🏗️ Engineering – to analyze change in materials or systems
Tips for Best Results
- Use
^for powers:x^2,e^x - Use
*for multiplication:2*x, not2x - Use parentheses for clarity:
sin((x^2 + 1)/2) - Use built-in symbols:
π,e,sqrt(),ln(),sin()
Frequently Asked Questions
❓ Can this calculator show step-by-step solutions?
Currently, it only shows the final derivative, not step-by-step differentiation. We may add that feature in the future.
❓ Does it support second or higher-order derivatives?
Not yet — we plan to add support for second, third, and nth derivatives soon.
❓ Can I graph the function?
This version does not have graphing, but it may be added later.
Final Words
This Derivative Calculator is designed for students, teachers, engineers, analysts, and curious minds who want quick and accurate derivative results.
No need to download any app or sign up. Just enter your function and get the result instantly!