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Mathematics

The Power Rule and Its Extension to Negative Exponents

Quick fact

The power rule works for any real exponent, not just positive integers. So d/dx(x^π) is simply π·x^(π−1), just as easily as for x².

Why this is interesting

You've mastered differentiating x², but what about 1/x²? The same simple rule works—surprisingly—even when exponents are negative. How is that possible?