How do you apply the power rule to find the derivative of ?
Conditions
- n is a fixed real exponent.
- Work on as the common real domain; positive integer powers extend over all real x and negative integer powers exclude .
- The source presents ; the constant case is treated separately.
Reasoning, step by step
- Identify the function .
- Bring the exponent n down to become the coefficient.
- Reduce the exponent by one to get n-1.
- Combine these to write the derivative as f'(x) = nx^{n-1].
Example
For , applying the rule with gives g'(x) = .
Common misconceptions
- Believing the power rule is proven in this lesson; the source explicitly states it is an application lesson with proofs deferred.
- Assuming the rule applies to without separate consideration; the source notes the constant case is treated separately.
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