What functions can I differentiate?
Monomials a·xⁿ and quadratics ax²+bx+c.
Derivative Calculator
Choose a monomial or quadratic, get f′(x), and optionally evaluate the derivative at x₀.
Enter the function
Select mode, enter coefficients, and optionally provide x₀.
About this calculator
How to use Derivative Calculator, plus the formulas and logic behind the results.
Tool description
Uses the power rule for monomials and the sum rule for quadratics. Optional point evaluation returns the slope of the tangent line at x₀.
How to use
- Choose power mode or quadratic mode.
- Enter the required coefficients (and n for power mode).
- Optionally enter x₀ to evaluate f′(x₀).
- Select Calculate to view f′(x) and any numeric value.
Formulas & reference
d/dx [a xⁿ] = a n xⁿ⁻¹d/dx [ax² + bx + c] = 2ax + b
Derivative tips
- Derivative of a constant is zero
- Power rule: bring down the exponent, reduce power by 1
- f′(x₀) is the slope of the tangent at x₀
- Quadratic mode ignores the n field
Calculation logic
Builds the symbolic derivative for the selected form and evaluates at x₀ when provided.
Covers common classroom cases only—not arbitrary symbolic expressions.
Derivative Calculator FAQ
Common questions about this calculator and how to use the results.
What is x₀ for?
Optional evaluation of the derivative (tangent slope) at that x-value.
What is the derivative of x²?
2x, from the power rule with a = 1 and n = 2.
Does quadratic mode need n?
No. Use a, b, and c only.
Are answers exact?
Symbolic derivatives are shown in simplified decimal coefficient form.
Can I use this for homework checks?
Yes—still show your own steps when required.