Continuity and Differentiability
Oswaal
CBSE
Grade 12
Question:
If $y = x^x$, then $\dfrac{dy}{dx}$ is equal to:
(a) $x^x (1 + \log x)$
(b) $x^x \log x$
(c) $x x^{x-1}$
(d) $1 + \log x$
Step-by-Step Solution
Key Concept: Logarithmic differentiation: d/dx x^x = x^x(1 + log x).
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: $x^x (1 + \log x)$
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