[tex]z=\sin\theta\cos\phi[/tex]
[tex]\theta=st^5[/tex]
[tex]\phi=s^7t[/tex]
[tex]\dfrac{\partial z}{\partial s}=\dfrac{\partial z}{\partial\theta}\dfrac{\partial\theta}{\partial s}+\dfrac{\partial z}{\partial\phi}\dfrac{\partial\phi}{\partial s}[/tex]
[tex]\dfrac{\partial z}{\partial s}=\cos\theta\cos\phi t^5-\sin\theta\sin\phi (7s^6t)[/tex]
[tex]\dfrac{\partial z}{\partial s}=t^5\cos(st^5)\cos(s^7t)-7s^6t\sin(st^5)\sin(s^7t)[/tex]
[tex]\dfrac{\partial z}{\partial t}=\dfrac{\partial
z}{\partial\theta}\dfrac{\partial\theta}{\partial t}+\dfrac{\partial
z}{\partial\phi}\dfrac{\partial\phi}{\partial t}[/tex]
[tex]\dfrac{\partial z}{\partial t}=\cos\theta\cos\phi(s5t^4)-\sin\theta\sin\phi s^7[/tex]
[tex]\dfrac{\partial z}{\partial t}=5st^4\cos(st^5)\cos(s^7t)-s^7\sin(st^5)\sin(s^7t)[/tex]
