Derivative Calculator

This calculator covers polynomials up to degree 3 (ax^3 + bx^2 + cx + d) with a clean interface. For higher-degree polynomials, set unused coefficients to 0. For quadratics, set a = 0. For linear functions, set a = 0 and b = 0.

The derivative f'(x) at a specific x gives the instantaneous rate of change, which is the slope of the tangent line to the curve at that point. A positive value means the function is increasing, negative means decreasing, and zero means a potential local maximum or minimum.

No. This calculator uses the polynomial power rule only. For derivatives of sin, cos, e^x, ln(x), and other functions, use a symbolic calculator or computer algebra system.

Yes. All coefficients accept any real number including decimals and negatives. The power rule applies identically regardless of coefficient sign or magnitude.

Set the derivative polynomial 3ax^2 + 2bx + c = 0 and solve the quadratic. The solutions are critical points where the original function may have local maxima, minima, or inflection points. This calculator evaluates f'(x) at a single point; solving for zeros requires the quadratic formula.

You can. Look for the "Embed" button near the top of this calculator. It lets you pick a size, border style, and color palette, then gives you an iframe tag to paste into any webpage. The widget is responsive, loads fast, and costs nothing. More details at calculory.com/services/embed-calculators.