Question

If $y^x-x^y=1,$ then the value of $\frac{dy}{dx}$ at $x=1$ is equal to

• A. $2(1-\ell n2)$
• B. $2+\ell n2$
• C. $2(1+\ell n2)$
• D. $2-\ell n2$

Answer 1

The correct option is A $2(1-\ell n2)$

$\frac{d}{dx}{y}^x-x^y=1⟹y^x\log y\frac{dy}{dx}-y{x}^{y-1}\frac{dy}{dx}=0$

At $x=1⟹y=2$

$\frac{dy}{dx}=2(1-\log 2)$