Find the derivative of any polynomial function with step-by-step power rule application.
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The most fundamental derivative rule: d/dx [xⁿ] = n·xⁿ⁻¹. Multiply by the exponent, then reduce the exponent by 1. This works for any real exponent.
The derivative of any constant is 0. Constants don't change, so their rate of change is zero.
The derivative of a sum (or difference) equals the sum (or difference) of derivatives. This lets us differentiate term by term.
Derivatives measure rates of change. They're used in physics (velocity, acceleration), economics (marginal cost), and everywhere optimization is needed.
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