요금제

미분 계산기

이 미분 계산기는 거듭제곱 법칙으로 다항식을 미분하며, 각 항의 도함수와 이계도함수를 보여 줍니다. 3x^3 - 2x + 5처럼 입력하세요.

거듭제곱에는 ^를 쓰세요 (x^2). (x+1)^2 같은 괄호도 됩니다

결과

값을 입력하고 계산을 누르면 결과가 표시됩니다.

공식

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.

이 계산기 사용법

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

풀이 예제

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.

자주 하는 실수

  • 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.

자주 묻는 질문

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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