If z = f(x,y)
(dz/dt) = (dx/dt) (dz/dx) + (dy/dt) (dz/dy)
Where dz/dx and dz/dy are partial derivatives.
I am not sure what fx(-5,1) = 1 and fy(-5,1) = -1 mean, but I guess they represent these partial derivatives. Summarizing the information until now:
g(1) = -5 –> x = -5 in this special case for t = 1
h(1) = 1 –> y = 1 in this special case for t = 1
g'(1) = -6
h'(1) = 1
for those specific values of x and y, the partial derivatives are:
dz/dx = 1
dz/dy = -1
Filling in gives:
(dz/dt) = (dx/dt) (dz/dx) + (dy/dt) (dz/dy)
dz/dt = -6 1 + 1 -1
dz/dt = -6 – 2
dz/dt = -8
Edit: I have to admit, that’s a bit stupid :). Thanks for correcting me!