# Crazy Partial derivative problem

• PsychonautQQ

## Homework Statement

Let W = F(u(s,t),v(s,t))

(in my notation, u_s would represent du/ds
u(1,0) = -7
v(1,0) = 3
u_s(1,0)=8
v_s(1,0)=5
u_t(1,0)=-2
v_t(1,0)=-4

F_u(-7,3)=-8
F_v(-7,3)=-2

Find W_s(1,0) and W_v(1,0)

Sort of having a hard time getting started here... I believe
W_s = df/du*du/ds + df/dv*dv/ds
and likewise for W_v...
I don't know how to make the knowledge of F_u(-7,3)=-8 and F_s(-7,3)=-2 useful though.

F_u=G(u(s,t),v(s,t))
When (s,t)=(1,0), we must evaluate:
F_u(u(1,0),s(1,0))

how do I do that with no actual equations X_x?

You have all the quantities you need calculate W_s.

To get you started
F_u(u(1,0),v(1,0))=F_u(-7,3)=-8
u_s(1,0)=8

so F_u*u_s=-8*8=64

And so on.

it doesn't matter that the coordinates change from (-7,3) to (1,0)?? I confused X_x

PsychonautQQ said:
it doesn't matter that the coordinates change from (-7,3) to (1,0)?? I confused X_x
(1,0) are (s,t)-coordinates, whereas (-7,3) are the corresponding (u,v)-coordinates.