Derivative of ln(x^5)
Answer
5*x^(-1)
Derivative of ln(x^5)
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in : use the chain rule = f'(g(x))·g'(x). The inner derivative is required because a stretch or shift of the input changes how fast the output moves.
- Differentiate the outer function, then multiply by the inner derivative.
- Final answer:
The derivative of ln(x^5) is 5*x^(-1).
Instant step-by-step solution for ln(x^5)
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Derivative of ln(x^5) = 5*x^(-1) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-lnx-minus-to-minus-the-minus-5
How to find the derivative of ln(x^5)
To find the derivative of ln(x^5), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
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Frequently Asked Questions
What is the derivative of ln(x^5)?▼
The derivative of ln(x^5) is 5*x^(-1).
How do you find the derivative of ln(x^5)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 5*x^(-1).
Why is the derivative of ln(x^5) equal to 5*x^(-1)?▼
Because differentiation measures how a function changes — applying the rules to ln(x^5) yields 5*x^(-1). See the full step-by-step breakdown above.