Higher Order Derivative Calculator

About this calculator

The nth derivative of a polynomial tells you how a rate of change is itself changing — the 2nd derivative gives acceleration when the 1st gives velocity, and so on. This calculator applies the power rule — d/dx[x^n] = n·x^(n−1) — repeatedly, n times, to a polynomial entered as a list of coefficients from the highest degree down.

Each application drops the degree by one and multiplies the coefficient by the current exponent, so a degree-5 polynomial differentiated 6 times collapses to zero — a quick way to see that the derivative order can't exceed the polynomial's degree without vanishing. This mirrors what a computer algebra system does symbolically, just done term by term.

It's useful for calculus students checking homework on higher-order derivatives, Taylor series coefficients, or curve concavity, and for anyone verifying a symbolic differentiation by hand.