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\( \text { If } 2 x^y+3 y^x=20 \text {, then } \frac{d y}{d x} \text { at }(2,2) \text { is equal to } \) [JEE Main 2023…

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

[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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