Abonnementen

Afgeleide-rekenmachine

Deze rekenmachine differentieert veeltermen met de machtsregel en toont de afgeleide van elke term en de tweede afgeleide. Typ iets als 3x^3 - 2x + 5.

Gebruik ^ voor machten (x^2); haakjes zoals (x+1)^2 mogen ook

Resultaat

Vul waarden in en tik op Berekenen om het resultaat te zien.

Formule

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.

Zo gebruik je deze rekenmachine

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

Uitgewerkte voorbeelden

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.

Veelgemaakte fouten

  • 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.

Veelgestelde vragen

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).

Meer informatie