JEE Main20236 Apr 2023Morning ShiftMathematicsDifferentiationActual

If 2 x y + 3 y x = 20 , then d y d x at 2 , 2 is equal to:

Options

A- 2 + log e 8 3 + log e 4
B- 3 + log e 16 4 + log e 8
C- 3 + log e 8 2 + log e 4
D- 3 + log e 4 2 + log e 8

Correct answer

A. - 2 + log e 8 3 + log e 4

Step-by-step solution

Given, 2 x y + 3 y x = 20 Now differentiating both sides w.r.t x , we get 2 x y y ' ln x + y x + 3 y x ln y + x y · y ' = 0 here  ln = log e Putting x = 2   &   y = 2 , we get ⇒ 8 ln 2 · y ' + 1 + 12 ln y + y ' = 0 ⇒ 8 ln 2 · y ' + 1 + 12 ln y + y ' = 0 ⇒ y ' = - 3 ln 2 + 2 2 ln 2 + 3 ⇒ y ' = - 2 + ln 8 3 + ln 4

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