Derivative (Power Rule) Calculator
Calculate the derivative of a term ax^n using the power rule. Shows the resulting coefficient and exponent.
f'(x) at given x
60.0000
Formule
## 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
Exemple Résolu
Find the derivative of 5x³ and evaluate at x = 2.
- 01d/dx [5x³] = 5 × 3 × x^(3-1) = 15x²
- 02f'(2) = 15 × 2² = 15 × 4 = 60
- 03f(2) = 5 × 2³ = 5 × 8 = 40
Questions Fréquentes
What is the power rule?
The power rule states that the derivative of x^n is n×x^(n-1). It works for any real exponent n, including negative and fractional values.
What is the derivative of a constant?
The derivative of any constant is 0. This follows from the power rule since a constant can be written as ax⁰, and 0 × ax^(-1) = 0.
Does the power rule work for negative exponents?
Yes. For example, d/dx [x^(-2)] = -2x^(-3) = -2/x³.
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