By the chain rule,
[tex]\dfrac{\partial w}{\partial u}=\dfrac{\partial w}{\partial x}\cdot\dfrac{\partial x}{\partial u}+\dfrac{\partial w}{\partial y}\cdot\dfrac{\partial y}{\partial u}+\dfrac{\partial w}{\partial z}\cdot\dfrac{\partial z}{\partial u}[/tex]
[tex]\dfrac{\partial w}{\partial u}=2xv+2y\cos v+2z\sin v[/tex]
We also have [tex]x(9,0)=0[/tex], [tex]y(9,0)=9[/tex], and [tex]z(9,0)=0[/tex], so at this point we get
[tex]\dfrac{\partial w}{\partial u}(9,0)=2\cdot9\cdot\cos0=18[/tex]
