Calculus Calculators
Second Derivative Calculator
Compute f″(x), the derivative of the derivative, with the sign explained.
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What is Second Derivative?
The second derivative is the rate of change of the slope: f″(x) tells you whether the curve is bending upward (concave up) or downward (concave down). Its sign change marks an inflection point, and its sign at a critical point is the second-derivative test.
How it works
The symbolic engine is applied twice, so the second derivative is exact whenever the function is in the grammar. Both derivatives are shown because the step from f′ to f″ is what the page is teaching.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.