Step-by-Step: The Power Rule
- Identify the exponent on your variable.
- Multiply the coefficient by that exponent.
- Subtract 1 from the exponent.
Worked Example
Differentiate f(x) = 3x⁴.
Multiply coefficient by exponent: 3 × 4 = 12.
Subtract 1 from exponent: 4 − 1 = 3.
f'(x) = 12x³
For a function with multiple terms like f(x) = 2x³ + 5x, apply the rule to each term separately: f'(x) = 6x² + 5.
Frequently Asked Questions
What's the derivative of a plain constant, like 7?
Zero — constants don't change, so their rate of change is always zero, regardless of the constant's value.
How do I handle a function with a negative exponent?
The power rule still applies directly — for f(x) = x⁻², the derivative is −2x⁻³, following the exact same "multiply by exponent, subtract one" process.
