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Power Rule for Derivatives

导数的幂函数求导法则

dxd​xn=nxn−1

Theoretical Identity Description:

The fundamental derivative rule for power functions. It states that the derivative of x^n with respect to x is n multiplied by x^(n-1).

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Rigorous Derivation Tree

2 Logical Steps
Step 1check_circleValid Deduction
dxd​xn=nxn−1

Foundational identity statement defined under standard mathematical conditions.

Step 2check_circleValid Deduction
dxd​xn=nxn−1

Targeted algebraic evaluation and parameter substitution.

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CSCA Exam Triggers & Traps

High-Yield Exam Focus
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Apply whenever an exam question presents conditions matching this canonical identity.

errorCommon Examination Pitfalls

Be vigilant of domain boundaries, sign flips, and degenerate boundary condition cases.

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Related Formulas in Derivatives

2 Formulas
Power Rule for Derivatives
导数的幂函数求导法则
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