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