Find the total derivative dz/dt, given

z=f(x,y,t) where x=a+bt and y=c+dt

3 answers

Without specifying the f(x,y,t) function, you can only give a general formula.

dz/dt(total) = �Ýz/�Ýx*dx/dt + �Ýz/�Ýy*dy/ dt + �Ýz/�Ýt
where all of the z derivatives on the right are partial derivatives.

dz/dt(total) = b �Ýz/�Ýx+ c �Ýz/�Ýy + �Ýz/�Ýt

I won't know if the �Ý symbol will display properly until I send this.
the "del" (slanted Greek d) symbol should have appeared where you see
�Ýz/
Idon't know this answer