Continuity and Differentiability
NCERT Class 12
CBSE
Grade 12
Question:
If $x^y = e^{x-y}$, then $\dfrac{dy}{dx}$ is equal to:
(a) $\dfrac{\log x}{(1 + \log x)^2}$
(b) $\dfrac{1}{(1 + \log x)^2}$
(c) $\dfrac{\log x}{1 + \log x}$
(d) $\dfrac{1 - \log x}{(1 + \log x)^2}$
Step-by-Step Solution
$y = \dfrac{x}{1+\log x} \Rightarrow y' = \dfrac{\log x}{(1+\log x)^2}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating derivative $= \log x/(1+\log x)^2$: 1.0 Mark
Correct Answer: $\dfrac{\log x}{(1 + \log x)^2}$
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