Answer
$\dfrac{\partial K}{\partial m}\dfrac{\partial^{2}K}{\partial v^{2}}=K$
Work Step by Step
$ \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
$\dfrac{\partial K}{\partial m}\dfrac{\partial^{2}K}{\partial v^{2}}=K$
