I am confuse. Please help.

Given w=sin xy + y ln xz + z, x=e^{t}and y =t^{2}. Use the method of partial differentiation to find dw/dt.

* Please show me the right solution for this so that i can compare it to my work. i am doubtful for my solution.

Iff(x,y,z)=xyz +x^{2}+ ln(y/z), prove thatf_{xyzx}=f_{zxxy}.