Derivative (Power Rule) Calculator — Formula
## 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
### 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
Exemplo Resolvido
Find the derivative of 5x³ and evaluate at x = 2.
- d/dx [5x³] = 5 × 3 × x^(3-1) = 15x²
- f'(2) = 15 × 2² = 15 × 4 = 60
- f(2) = 5 × 2³ = 5 × 8 = 40