purr.tools

Derivative Calculator

Enter a polynomial expression to compute its derivative using the power rule. Supports sums and differences of terms like 3x^2 + 2x - 5.

Supports polynomial terms: ax^n, ax, constants. Use ^ for exponents.

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How to use the derivative calculator

Type a polynomial expression using standard notation: coefficients followed by x^power. Use + and - to combine terms. Examples: x^3 - 4x^2 + 7, 0.5x^4 + 3x - 1. The calculator applies the power rule to each term.

The power rule

The derivative of ax^n is n*a*x^(n-1). The derivative of a constant is 0. The derivative of ax is a. These rules apply term-by-term to polynomial sums.

FAQ

What expressions are supported?

Polynomial expressions with non-negative integer or decimal exponents: terms like 3x^2, x^5, 4x, -2x^0.5, or constants. Expressions with negative exponents, parentheses, trigonometric, or logarithmic functions are not supported.

Why does the tool show an error?

The parser expects standard polynomial notation. Check that you use ^ for exponents, don't include multiplication signs (*), and avoid unsupported functions or negative exponents like x^-2.

Embed this tool

Add this tool to your website by copying the snippet below.

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  src="https://purr.tools/en/embed/derivative-calculator"
  width="100%"
  height="500"
  style="border:0;border-radius:8px;"
  loading="lazy"
  title="Derivative Calculator -- Free Online Tool"
  allow="clipboard-write"
></iframe>