Calcolatrice di derivate
Questa calcolatrice deriva polinomi con la regola della potenza, mostrando la derivata di ogni termine e la derivata seconda. Scrivi per esempio 3x^3 - 2x + 5.
Risultato
Inserisci i valori e premi Calcola per vedere il risultato.
Formula
The power rule: bring the power down and reduce it by one.
Come usare questa calcolatrice
- Type the polynomial. Implicit multiplication like 3x or 2(x+1) works.
- Press Calculate.
Esempi svolti
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.
Errori comuni
- 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.
Domande frequenti
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).