$(5)[10$ Points$]$ Given a function $f(t^{2}1,4t-8,t{e}^{t-1})$ with partial derivative evaluations $f_x(2,-4,1)=1,f_y(2,-4,1)=-1,$ and $f_z(2,-4,1)=5,$ calculate $\frac{df}{dt}$ at the point $(2,-4,1).$