Derivative Calculator

Enter the coefficients of a polynomial (up to degree 4) and a point x, and this tool differentiates it term-by-term using the power rule.

Coefficient a (of x⁴)

Coefficient b (of x³)

Coefficient c (of x²)

Coefficient d (of x¹)

Coefficient e (constant)

Evaluate derivative at x =

What this calculator does

This tool finds the derivative of a polynomial function f(x) = ax⁴ + bx³ + cx² + dx + e and evaluates it at a point of your choosing. Just fill in the coefficients that match your function (leave any term as 0 if it isn’t present).

The method: the power rule

Each term is differentiated separately using the standard power rule, d/dx[xⁿ] = n·xⁿ⁻¹. That gives f'(x) = 4ax³ + 3bx² + 2cx + d. The calculator then substitutes your chosen x-value into f'(x) to report the instantaneous slope of the original function at that point.

Set higher-degree coefficients to 0 to differentiate a simpler polynomial (linear, quadratic, or cubic).
The result is the exact slope of the tangent line to f(x) at x, not an approximation.

This calculator is provided for general educational and planning purposes.

Last reviewed August 2026