Continuity and Differentiability
NCERT Class 12
CBSE
Grade 12
Question:
If $x^y + y^x = b^a$, find $\dfrac{dy}{dx}$.
Step-by-Step Solution
$\dfrac{du}{dx} = x^y (y/x + \log x \cdot y')$, $\dfrac{dv}{dx} = y^x ((x/y)y' + \log y)$. [1.5 Marks]
$y' = -\dfrac{y x^{y-1} + y^x \log y}{x^y \log x + x y^{x-1}}$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Evaluating logarithmic derivatives of $u$ and $v$: 1.5 Marks
Collecting terms and solving $dy/dx$: 1.5 Marks
Correct Answer:
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