[tex]\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}[/tex]
[tex]=2x\left(\dfrac3t\right)+2y\left(-\sin t\right)[/tex]
[tex]=2(3\ln t)\left(\dfrac3t\right)+2\cos t(-\sin t)[/tex]
[tex]=\dfrac{18\ln t}t-2\cos t\sin t[/tex]
[tex]=\dfrac{18\ln t}t-\sin2t[/tex]
