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Derivative Calculator
Enter an expression in x and get its symbolic derivative, simplified, with the differentiation rules used listed step by step. Runs entirely in your browser.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Example shown - supports + - * / ^, sin, cos, tan, exp, ln, sqrt, and parentheses.
f′(x)
Rules applied
How the derivative calculator works
- Type an expression in x using standard notation, e.g.
x^3 + 2*x^2 - sin(x). - The tool parses it into an expression tree and applies the relevant differentiation rule to each part.
- The result is simplified and shown alongside the list of rules that were applied.
The method
Each expression is parsed into a tree of operations, then differentiated recursively: sums differentiate term by term, products use the product rule, quotients use the quotient rule, and powers with constant exponents use the power rule. Trig, exponential, and logarithmic functions each apply their own known derivative combined with the chain rule for their inner expression.
d/dx[xⁿ] = n·x^(n-1) | d/dx[uv] = u'v + uv' | d/dx[u/v] = (u'v - uv')/v²
FAQ
What functions are supported?
Polynomial terms, +, -, *, /, ^ with a constant exponent, and the functions sin, cos, tan, exp, ln, and sqrt, with parentheses for grouping.
Why does x^x or x^(sin(x)) fail?
Those need logarithmic differentiation, which this tool does not implement. Only constant exponents (like x^3) are supported by the power rule path.
Does the result get simplified?
Yes, with basic algebraic simplification - removing multiplication by 1, addition of 0, and folding constant arithmetic - but it is not a full computer-algebra simplifier, so some results may not be in the most compact form possible.
Is my expression sent to a server?
No. Parsing, differentiation, and simplification all happen locally in your browser using a small JavaScript expression engine.
How we compare
| Feature | Online Tool Store | Symbolab | Wolfram Alpha |
|---|---|---|---|
| No sign-up or step limit | ✓ | Steps require subscription | Steps require Pro |
| Expression stays in your browser | ✓ | ✗ | ✗ |
| Free, no ads | ✓ | ✗ | ✗ |
For quick homework-style derivatives with the rules shown for free, Derivative Calculator gets you there without a paywall.