## Calculus 8th Edition

$\dfrac{\partial K}{\partial m}\dfrac{\partial^{2}K}{\partial v^{2}}=K$
$\dfrac{\partial K}{\partial m}=\dfrac{\partial}{\partial m}[\dfrac{1}{2}mv^{2}]=\dfrac{1}{2}v^{2}$ ...(1) $\dfrac{\partial K}{\partial v}=\dfrac{\partial}{\partial v}[(\dfrac{1}{2})mv^{2}]=mv$ ...(2) From the equations (1) and (2), we have $\dfrac{\partial^{2}K}{\partial v^{2}}=\dfrac{\partial}{\partial v}[mv]=m$ and $\dfrac{\partial K}{\partial m}\times\dfrac{\partial^{2}K}{\partial v^{2}}=\dfrac{1}{2} \times (mv^{2})=K$ After solving, we get $\dfrac{\partial K}{\partial m}\dfrac{\partial^{2}K}{\partial v^{2}}=K$