How to use this calculator
For polynomial modes, enter coefficients highest power first, then x or integration bounds. For numerical modes, enter f(x) and a point or bounds.
Formula and method
d(a xⁿ)/dx = n a xⁿ⁻¹; ∫a xⁿ dx = a xⁿ⁺¹/(n+1)+C. Numerical integration uses composite Simpson’s rule; derivative uses five-point central differences.
Worked example
For 3x²−2, derivative at x=2 is 12; integral from 0 to 2 is 4; limit at 2 is 10.
Assumptions and supported scope
Polynomial degree ≤7, real finite coefficients. Numerical expressions ≤160 characters; integration uses 400 panels and interval width ≤1,000,000. Numerical derivative/limit are estimates that need local smoothness or convergence; discontinuities, oscillations, and poles may defeat sampling. No symbolic general-function differentiation.
Method references
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