Question:
(d) If \( y = x^x \), then find \( \frac{dy}{dx} \).
(d) If \( y = x^x \), then find \( \frac{dy}{dx} \).
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For expressions like \( y = x^x \), use logarithmic differentiation.
Updated On: Mar 3, 2025
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Solution and Explanation
Take the logarithm of both sides:
\[ \ln y = x \ln x. \]Differentiate with respect to \( x \):
\[ \frac{1}{y} \frac{dy}{dx} = \ln x + 1. \]Multiply through by \( y = x^x \):
\[ \frac{dy}{dx} = x^x (\ln x + 1). \]Was this answer helpful?
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