JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(2 x^y+3 y^x=20\), then \(\frac{d y}{d x}\) at \((2,2)\) is equal to
- 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 \(-\left(\frac{3+\log _e 4}{2+\log _e 8}\right)\)
Answer & Solution
Correct Answer
(B) \(-\left(\frac{2+\log _e 8}{3+\log _e 4}\right)\)
Step-by-step Solution
Detailed explanation
\(2 x^y+3 y^x=20\) \(2 x^y\left[\frac{y}{x}+(\ln x) y^{\prime}\right]+3 y^x\left[\frac{x y^{\prime}}{y}+\ln y\right]=0\) \(y^{\prime}=\frac{-(12 \ln 2+8)}{12+8 \ln 2}=-\left(\frac{2+\log _e 8}{3+\log _e 4}\right)\)
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