Second Derivative Calculator

Enter a polynomial and instantly get its second derivative f''(x) with step-by-step power rule working.

Use the Second Derivative Calculator

Enter Polynomial

Use ^ for exponents, e.g. 4x^3 + 2x^2 - 5x + 8

Quick Examples

Enter a polynomial and click Calculate to see f'(x) and f''(x).

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Summary

This second derivative calculator applies the power rule twice to find f''(x) for any polynomial expression, entirely in your browser. Enter a polynomial with integer or fractional exponents and see the first derivative f'(x) computed step by step, followed by the second derivative f''(x) — no server, no signup required.

How it works

  1. Type a polynomial expression in the input field, e.g. 4x^3 + 2x^2 - 5x + 8.
  2. Click "Calculate" or press Enter to start.
  3. The power rule d/dx[ax^n] = n·ax^(n−1) is applied to each term to get f'(x).
  4. The power rule is applied a second time to f'(x) to produce f''(x).
  5. All working for both differentiation passes is displayed in a numbered step list.
  6. Copy either result with one click.

Use cases

  • Verify second derivative homework answers for polynomial functions.
  • Find where a curve is concave up or concave down using the second derivative sign.
  • Apply the second derivative test to classify critical points as minima or maxima.
  • Check acceleration expressions derived from a polynomial position function.
  • Teach or visualize double differentiation step by step for calculus students.
  • Quickly confirm d²y/dx² before substituting into a physics or engineering formula.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu