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If \(2 x^y+3 y^x=20\), then \(\frac{d y}{d x}\) at \((2,2)\) is equal to [JEE Main 2023, 6 Apr (Shift 1)]

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If \(2 x^y+3 y^x=20\), then \(\frac{d y}{d x}\) at \((2,2)\) is equal to

[JEE Main 2023, 6 Apr (Shift 1)]

a

\(-\left(\frac{3+\log _e 8}{2+\log _e 4}\right)\)

b

\(-\left(\frac{2+\log _e 8}{3+\log _e 4}\right)\)

c

\(-\left(\frac{3+\log _e 16}{4+\log _e 8}\right)\)

d

\(-\left(\frac{3+\log _e 4}{2+\log _e 8}\right)\)

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