Mga plan

Derivative at Differentiation Calculator

Nagdi-differentiate ng mga polynomial ang calculator na ito gamit ang power rule, at ipinapakita ang derivative ng bawat termino at ang second derivative. Mag-type ng gaya ng 3x^3 - 2x + 5.

Gamitin ang ^ para sa power (x^2); puwede rin ang panaklong gaya ng (x+1)^2

Resulta

Ilagay ang mga halaga at pindutin ang “Kuwentahin” para makita ang resulta.

Formula

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.

Paano gamitin ang calculator na ito

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

Mga halimbawang may solusyon

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.

Mga karaniwang pagkakamali

  • 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.

Mga madalas itanong

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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