幂法则求导计算器 — 公式

Power Rule for Derivatives

Rule

d/dx [ax^n] = a × n × x^(n-1)

The power rule is the most fundamental differentiation rule: 1. Bring the exponent down as a multiplier 2. Reduce the exponent by 1

Examples

  • d/dx [5x³] = 15x²
  • d/dx [x²] = 2x
  • d/dx [7x] = 7
  • d/dx [constant] = 0

    • 计算示例

    Find the derivative of 5x³ and evaluate at x = 2.

    1. d/dx [5x³] = 5 × 3 × x^(3-1) = 15x²
    2. f'(2) = 15 × 2² = 15 × 4 = 60
    3. f(2) = 5 × 2³ = 5 × 8 = 40