Derivative of x^ln(x)
Answer
2*ln(x)*x^(-1+ln(x))
Derivative of x^ln(x)
- Rule Used
- Power Rule
- Steps
- Identify the expression as a power function and apply the power rule. A rational exponent is allowed: ^(p/q) = (p/q)·.
- Final answer: n(x)*
The derivative of x^ln(x) is 2*ln(x)*x^(-1+ln(x)).
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Derivative of x^ln(x) = 2*ln(x)*x^(-1+ln(x)) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-lnx
How to find the derivative of x^ln(x)
To find the derivative of x^ln(x), 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 x^ln(x)?▼
The derivative of x^ln(x) is 2*ln(x)*x^(-1+ln(x)).
How do you find the derivative of x^ln(x)?▼
Apply the standard differentiation rules — the key rule used here is the Power Rule. The step-by-step result is 2*ln(x)*x^(-1+ln(x)).
Why is the derivative of x^ln(x) equal to 2*ln(x)*x^(-1+ln(x))?▼
Because differentiation measures how a function changes — applying the rules to x^ln(x) yields 2*ln(x)*x^(-1+ln(x)). See the full step-by-step breakdown above.