Am kinda stuck with this function They gave me;

f(x,t)=ln(x^2(t)-t/x)

am asked for all first and second order partial dervitves to make the function simpller i did this

f(x,t)=ln(x^2(t)(1-1/x^3))

to break up the to ln's

i get now =ln(x^2t)+ln(1-1/x^3)

for my second order fxy=0 and for fyx=0 i need someone to confirm these for me is my alebgra correct is what am doing correctby splitting up to logarathimes thank you for ur help!