• # question_answer If ${{y}^{x}}-{{x}^{y}}=1,$ then the value of $\frac{dy}{dx}$ at $x=1$ is A)  $2(1-\log \,2)$            B)  $2(1+\,\log \,2)$ C)  $2-\log \,2$                 D)  $2+\log \,2$

${{N}_{S}}=\left( \frac{\rho S}{\rho P} \right)\times {{N}_{P}}$ Put $=\frac{(4.4\times {{10}^{3}})\,\times 100}{220}=2000$ we get${{\rho }_{S}}$ One differentiating both sides w.r.t. x, we get ${{\rho }_{P}}$ $-h=-u{{t}_{1}}+\frac{1}{2}gt_{1}^{2}$          $-h=-u{{t}_{2}}+\frac{1}{2}gt_{2}^{2}$ $0=u({{t}_{2}}-{{t}_{1}})+\frac{1}{2}g(t_{1}^{2}-t_{2}^{2})$ $u=\frac{1}{2}g({{t}_{1}}+{{t}_{2}})$  $h=\frac{g{{t}_{1}}{{t}_{2}}}{2}$