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To apply the power rule, bring the fixed exponent n down as a coefficient and reduce the exponent by one, yielding f'(x) = nx^{n-1}. The source presents this as an application shortcut for its displayed $n\ne 0$ examples, deferring proofs to later lessons.

Conditions: n is a fixed real exponent.; Work on $x>0$ as the common real domain; positive integer powers extend over all real x and negative integer powers exclude $x=0$.; The source presents $n\ne 0$; the constant $n=0$ case is treated separately.

To apply the power rule, bring the fixed exponent n down as a coefficient and reduce the exponent by one, yielding f'(x) = nx^{n-1}. The source presents this as an application shortcut for its displayed $n\ne 0$ examples, deferring proofs to later lessons.

Conditions: n is a fixed real exponent.; Work on $x>0$ as the common real domain; positive integer powers extend over all real x and negative integer powers exclude $x=0$.; The source presents $n\ne 0$; the constant $n=0$ case is treated separately.

To find the derivative of a polynomial function like $f(x) = x^2$, identify the exponent n and apply the power rule f'(x) = nx^{n-1}. Bring the exponent down as a coefficient and reduce it by one.

Conditions: n is a fixed real exponent.; Use $x>0$ as the common real domain; positive integer powers extend over all real x and negative integer powers exclude $x=0$.; The source presents $n\ne 0$; the constant $n=0$ case is treated separately.

To find the derivative of a polynomial function like $f(x) = x^2$, identify the exponent n and apply the power rule f'(x) = nx^{n-1}. Bring the exponent down as a coefficient and reduce it by one.

Conditions: n is a fixed real exponent.; Use $x>0$ as the common real domain; positive integer powers extend over all real x and negative integer powers exclude $x=0$.; The source presents $n\ne 0$; the constant $n=0$ case is treated separately.