For any fixed exponent n, the derivative of xn brings the exponent down as a multiplier and reduces it by one:
dxd[xn]=nxn−1
This works for negative and fractional exponents too, not just positive whole numbers.
Worked example
Find the derivative of f(x)=x.
Solution: Rewrite the square root as a fractional exponent, f(x)=x1/2, then apply the power rule with n=21:
f′(x)=21x21−1=21x−21
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The power rule only differentiates a single power of x, once two functions are multiplied or divided together, the product rule or quotient rule takes over.