What is the Derivative Calculator?
Compute symbolic derivatives of functions in one variable with step-by-step differentiation rules. Enter expressions like x^3 + 2x^2 - 5x + 1, sin(x), or x^2*sin(x). The calculator applies sum, product, quotient, power, and chain rules for sin, cos, tan, ln, log, sqrt, exp, and abs. Choose 1st or 2nd derivative. Free, private, and instant in your browser.
How to use the Derivative Calculator
- Enter a function of your variable (e.g. x^3 + 2*x^2 - 5*x + 1).
- Set the variable letter if it is not x.
- Choose 1st or 2nd derivative.
- Read the symbolic result and differentiation steps.
- Copy the result for homework or notes.
Common use cases
- Checking calculus homework derivatives
- Finding the slope function f'(x) from a polynomial
- Practicing product and chain rule on sin(x^2) or x^2*sin(x)
Frequently asked questions
- What functions are supported?
- Polynomials, sin, cos, tan, ln, log (base 10), sqrt, exp, abs, constants pi and e, and combinations with +, −, ×, ÷, and powers.
- How do I write multiplication?
- Use * explicitly (2*x) or write 2x — implicit multiplication is supported.
- Can I find second derivatives?
- Yes. Switch to 2nd derivative mode to differentiate the result again symbolically.
- Is the output simplified?
- Basic simplification is applied (combining constants, removing +0 and *1). Results may still be expanded rather than factored.
