Calculate ∂f/∂s+ ∂f/∂t at s = 2, t = −1, given that
f=f(x,y); x=s−t, y=s2+t2, ∂f/∂x(3,5)=0.06170, ∂f/∂y(3,5)=0.06170.

Question

Calculate ∂f/∂s+ ∂f/∂t at s = 2, t = −1, given that 
f=f(x,y); x=s−t, y=s2+t2, ∂f/∂x(3,5)=0.06170,   ∂f/∂y(3,5)=0.06170.

anonymous · Answer

∂f/∂s= ∂f/∂x  dx/ds +∂f/∂y  dy/ds

anonymous · Answer

∂f/∂s= ∂f/∂x         dx/ds +∂f/∂y       dy/ds
             0.06170     1       +0.06170   2s

anonymous · Answer

∂f/∂t= ∂f/∂x         dx/dt +∂f/∂y       dy/dt
           0.06170    (  -1)  +.0617      2t

zarkon · Answer

just notation, but we should write 

$$\frac{\partial f}{\partial s}=\frac{\partial f}{\partial x}\frac{\partial x}{\partial s}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial s}$$

since x and y are functions of more than one variable

turingtest · Answer

now do you get the partial symbols?

zarkon · Answer

\partial

turingtest · Answer

$$/\partial$$thanks!

anonymous · Answer

ok thanks for the help... just one more question. how do you know that ∂f/∂s= ∂f/∂x?

anonymous · Answer

nvm, i got it now. thanks