About the Derivative Calculator
The derivative of a function tells you its slope at every point. For a polynomial, the rule is simple: multiply each term by its power and lower the power by one. This calculator applies the rule to any polynomial in x that you type. It also gives the second derivative and, if you enter a value of x, the value of the function, its slope and its curvature at that point. Type a polynomial in x and, optionally, a value of x and the derivative of a polynomial appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Derivative Calculator
- 1Enter a polynomial in x and, optionally, a value of x.
- 2Pick the units or options from the menus if the derivative of a polynomial tool offers them.
- 3Read the derivative of a polynomial in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the derivative of a polynomial
Students use it to check differentiation homework and to find where a curve is steepest, rising or falling. Setting the derivative to zero finds the peaks and valleys, which is the first step in many optimisation problems in physics, economics and engineering.
Write powers with a caret, as in x^3. Multiplication signs and spaces are optional, so 2x^2, 2*x^2 and 2 x^2 are the same. Like terms are collected, so x + x + 3x becomes 5x.
How the derivative of a polynomial is worked out
Power rule: the derivative of c·xⁿ is n·c·xⁿ⁻¹. Constants have derivative 0. The derivative of a sum is the sum of the derivatives. For 3x² + 2x − 5 the derivative is 6x + 2 and the second derivative is 6. At x = 2 the function equals 11, its slope is 14, and the curvature is 6. For x³ − 4x + 1 the derivative is 3x² − 4.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Power rule for polynomials
- Second derivative
- Value and slope at a point
Mistakes to avoid with derivative of a polynomial
The calculator handles polynomials with whole-number powers from 0 to 50. It does not handle sine, cosine, logarithms, fractions with x in the bottom or negative powers; those need other rules. If the input cannot be read, a message names the part it could not understand.
On phone and computer
On a phone, type into the boxes one after another and read the derivative of a polynomial underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the derivative of a polynomial move. The derivative calculator works the same on both. Maths tools work together. Integral Calculator reverses the step, Slope Calculator is the simple version, and Quadratic Equation Solver and Cubic Equation Solver find where the function is zero.
Features
- Use ^ for powers
- Whole-number powers only
- Zero derivative marks turning points
- Clear messages when the derivative of a polynomial inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate derivative of a polynomial?
Power rule: the derivative of c·xⁿ is n·c·xⁿ⁻¹. Constants have derivative 0. The derivative of a sum is the sum of the derivatives. For 3x² + 2x − 5 the derivative is 6x + 2 and the second derivative is 6. At x = 2 the function equals 11, its slope is 14, and the curvature is 6. For x³ − 4x + 1 the derivative is 3x² − 4.
What is the formula for derivative of a polynomial?
Power rule: the derivative of c·xⁿ is n·c·xⁿ⁻¹. Constants have derivative 0. The derivative of a sum is the sum of the derivatives. The derivative calculator applies it exactly and rounds only the displayed answer to six significant figures.
What does the derivative mean?
The rate of change, or the slope of the curve at a point.
What is the derivative of a constant?
Zero, because a constant does not change.
How do I find a maximum or minimum?
Set the derivative to zero and solve. The sign of the second derivative tells whether it is a minimum (positive) or a maximum (negative).
Is this derivative calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.