Calculus

Derivative: Power Rule

Formula

d/dx [xⁿ] = n × xⁿ⁻¹

What is Derivative: Power Rule?

The power rule is the most commonly used differentiation rule. To find the derivative of x raised to a power, bring the exponent down as a coefficient and decrease the exponent by 1.

Variables

x
x — The variable
n
n — The exponent (any real number)

Worked Examples

Example 1

Find the derivative of x⁵.

Solution:

d/dx [x⁵] = 5x⁴

Example 2

Find the derivative of x³ + 2x² + x.

Solution:

d/dx = 3x² + 4x + 1

Frequently Asked Questions

Related Formulas

Derivative: Product Rule

(fg)' = f'g + fg'

Derivative: Quotient Rule

(f/g)' = (f'g − fg') / g²

Derivative: Chain Rule

d/dx [f(g(x))] = f'(g(x)) × g'(x)

Integral: Power Rule

∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)

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