Softonic

Polynomial Derivative Calculator

Step 1 / 4 Polynomial derivative

Need a quick check on a polynomial derivative? Enter an expression like 3x^3 + 2x^2 - 5x + 7 and the calculator applies the power rule term by term to return f'(x).

How to differentiate a polynomial

  1. 1

    Enter a polynomial in x

    Use terms such as `4x^4`, `2x^2`, `-5x` and constants. The calculator reads powers of the variable `x`.

  2. 2

    Keep the syntax simple

    Write `3x^3`, not `3*x^3`; expand parentheses before entering the expression.

  3. 3

    Read the derivative

    Each power term is differentiated with the power rule, linear terms become constants, and standalone constants drop out.

  4. 4

    Check the limits

    For trigonometric functions, logarithms, products, quotients or implicit differentiation, use a full symbolic algebra tool.

What the calculator differentiates

Input pattern Rule used Example result
c Constant rule: d/dx [c] = 0 7 contributes 0
ax Linear term: d/dx [ax] = a -5x becomes -5
ax^n Power rule: d/dx [ax^n] = a * n * x^(n-1) 3x^3 becomes 9x^2
Sums and differences Differentiate each term separately 3x^3 + 2x^2 - 5x becomes 9x^2 + 4x - 5
Decimal coefficients Use a decimal point in the coefficient 1.5x^2 becomes 3x

Worked example

For f(x) = 3x^3 + 2x^2 - 5x + 7:

  1. 3x^3 uses the power rule: 3 * 3x^2 = 9x^2.
  2. 2x^2 becomes 4x.
  3. -5x becomes -5.
  4. The constant 7 becomes 0.

So the derivative is f'(x) = 9x^2 + 4x - 5.

Tips for clean input

  • Use x as the variable. Other letters are not treated as symbolic variables by this lightweight calculator.
  • Write powers with ^ and whole-number exponents: x^4, 12x^2, 0.5x^3.
  • Expand products first. Enter x^2 + x instead of x(x+1).
  • Use a decimal point for coefficients when needed, such as 0.5x^2, rather than fractions in parentheses.

Limitations

  • This is a polynomial power-rule checker, not a full computer algebra system.
  • It does not parse sin(x), ln(x), quotients, parentheses, negative exponents, implicit differentiation or piecewise functions.
  • To find a second derivative, copy the first derivative back into the input and differentiate again.

Frequently Asked Questions

No. This calculator is focused on single-variable polynomials in x. For partial derivatives with several variables, use a full symbolic algebra tool.

Standalone constants differentiate to zero. A term can also be skipped if it uses unsupported syntax, such as another variable, parentheses or a function name.

There is no separate order selector. Differentiate once, copy the result back into the input, and run it again for the next derivative.

The expression is processed by the web app so it can return the visible result. Do not enter confidential or sensitive formulas.

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