AP EAMCET · Maths · Differentiation
If \(x^x y^y=e^e\), then \(\left(\frac{d^2 y}{d x^2}\right)_{(e, e)}=\)
- A \(\frac{1}{e}\left(\frac{d y}{d x}\right)_{(e, e)}\)
- B \(\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{(\mathrm{e}, \mathrm{e})}+\frac{1}{\mathrm{e}}\)
- C \(\left(\frac{d y}{d x}\right)_{(e, e)}-\frac{1}{e}\)
- D \(e\left(\frac{d y}{d x}\right)_{(e, e)}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{e}\left(\frac{d y}{d x}\right)_{(e, e)}\)
Step-by-step Solution
Detailed explanation
Given \(x^x y^y=e^e\) Since \(\ln \left(x^x y^y\right)=\ln \left(e^e\right)\) \(\Rightarrow x \ln (x)+y \ln (y)=e\) Differentiating with respect to \(\mathrm{x}\).…
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