Aspire Faculty ID #13522 · Topic: JAMIA MILLIA ISLAMIA MCA 2024 · Just now
JAMIA MILLIA ISLAMIA MCA 2024

If $x^{,y}y^{,x}=16$, then $\left.\dfrac{dy}{dx}\right|_{(2,2)}$ is

Solution

$\ln(x^{y}y^{x})=y\ln x+x\ln y=\ln16$ $\Rightarrow y'(\ln x+\tfrac{x}{y})+(\tfrac{y}{x}+\ln y)=0$ At $(2,2)$: $y'=\dfrac{-,(1+\ln2)}{,\ln2+1}=-1.$
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