Tarife

Ableitungsrechner

Dieser Rechner leitet Polynome mit der Potenzregel ab und zeigt die Ableitung jedes Terms sowie die zweite Ableitung. Gib etwa 3x^3 - 2x + 5 ein.

Verwende ^ für Potenzen (x^2); Klammern wie (x+1)^2 sind erlaubt

Ergebnis

Gib Werte ein und tippe auf Berechnen, um das Ergebnis zu sehen.

Formel

ddx axn=naxn−1\frac{d}{dx}\,a x^n = n a x^{n-1}

The power rule: bring the power down and reduce it by one.

So benutzt du diesen Rechner

  1. Type the polynomial. Implicit multiplication like 3x or 2(x+1) works.
  2. Press Calculate.

Gelöste Beispiele

Differentiate 3x³ − 2x + 5

3x³ → 9x², −2x → −2, and the constant 5 → 0.

So f′(x) = 9x² − 2 and f″(x) = 18x.

Medium: x⁴ − 3x² + 7

Power rule term by term: x⁴ → 4x³, −3x² → −6x, and the constant 7 → 0.

f′(x) = 4x³ − 6x. Differentiating again: f″(x) = 12x² − 6.

Hard: a power of a bracket, (2x + 1)³

Expand first: (2x + 1)³ = 8x³ + 12x² + 6x + 1.

Differentiate: f′(x) = 24x² + 24x + 6. The chain rule gives the same: 3(2x + 1)² × 2 = 6(4x² + 4x + 1).

f″(x) = 48x + 24.

Häufige Fehler

  • Forgetting to multiply by the old power: the derivative of x⁴ is 4x³, not x³.
  • Keeping the constant: the derivative of a constant such as 7 is 0.
  • Differentiating (2x + 1)³ as 3(2x + 1)² without the chain-rule factor 2.

Häufig gestellte Fragen

What does a differentiate calculator do?

It finds the derivative — the rate of change, or the slope of the tangent — of a function. For polynomials this is the power rule applied to every term.

Which functions are supported?

Polynomials (powers of one variable). For sin, eˣ or ln, use Sumzo AI.

What is the second derivative?

The derivative of the derivative — it describes how the slope itself changes (concavity).

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