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

Option 4: $-\left(\frac{2+\log_e 8}{3+\log_e 4}\right)$

$-\left(\frac{3+\log_e 4}{2+\log_e 8}\right)$

$-\left(\frac{3+\log_e 16}{4+\log_e 8}\right)$

$-\left(\frac{3+\log_e 8}{2+\log_e 4}\right)$

$-\left(\frac{2+\log_e 8}{3+\log_e 4}\right)$

JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2023, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

2x^y+3y^x=20

, then

\frac{dy}{dx}

(2,2)

is equal to:

(1) $-\left(\frac{3+\log_e 4}{2+\log_e 8}\right)$
(2) $-\left(\frac{3+\log_e 16}{4+\log_e 8}\right)$
(3) $-\left(\frac{3+\log_e 8}{2+\log_e 4}\right)$
(4) $-\left(\frac{2+\log_e 8}{3+\log_e 4}\right)$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Continuity and Differentiability
Topic: Chain Rule
Idea tested: Logarithmic Differentiation of Composite Products

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.