Question

$If{x}^{cosy}+y^{cosx}=5.$ Then

• A. at x = 0, y = 0, y’ = 0
• B. at x = 0, y = 1, y’ = 0
• C. at x = y = 1, y’ = – 1
• D. at x = 1, y = 0, y’ = 1

Answer 1

The correct option is C at x = y = 1, y’ = – 1

$x^{cosy}+y^{cosx}=5$
$\Rightarrow e^{cosylo{g}_{e}x}+e^{cosxlo{g}_{e}y}=5$
$\therefore e^{cosylo{g}_{e}x}\{\frac{cosy}{x}-lo{g}_{e}x(siny\left)\frac{dy}{dx}\right\}+e^{cosxlo{g}_{e}y}\{\frac{cosx}{y}\frac{dy}{dx}-sinxlo{g}_{e}y\}=0$
$Putx=y=1,(cos1-0)+(cos1\frac{dy}{dx}-0)=0$
$\therefore \frac{dy}{dx}=-1$
$or{y}^{\prime }=-1$