What is the Derivative Calculator?
The derivative calculator is a free online tool that helps you work out derivative quickly and accurately. It uses the standard formula Symbolic differentiation with respect to the variable and shows the result instantly as you type, along with a full breakdown so you can see exactly how the answer was reached.
How to use this calculator
- Enter f(x).
- Set the variable.
- Optionally evaluate at a point.
- See the derivative.
Formula used
Symbolic differentiation with respect to the variableExplanation of each input
- Function f(x) โ the function f(x) used in the calculation.
- Variable โ the variable used in the calculation.
- Evaluate at x = โ the evaluate at x = used in the calculation.
Understanding your result
- Derivative โ the calculated derivative.
- Value at point โ the calculated value at point.
Step-by-step calculation
For the example values x^2 + 3x:
- Apply the formula:
Symbolic differentiation with respect to the variable - Substitute the values: d/dx
- Result: 2x + 3
Worked example
| Inputs | x^2 + 3x |
|---|---|
| Working | d/dx |
| Result | 2x + 3 |
Benefits and practical uses
This calculator saves you time and reduces errors when you need derivative. It is useful for students, professionals and anyone who wants a fast, reliable answer without manual calculation. Results update instantly, work in your browser and can be copied or shared in one click.
Assumptions and limitations
- Differentiable expression.
Frequently asked questions
What is a derivative?
The instantaneous rate of change of a function - its slope at each point.
Disclaimer: Results are provided for general information. Please verify important figures independently.