English Deutsch Français Italiano Español Português 繁體中文 Bahasa Indonesia Tiếng Việt ภาษาไทย
All categories

I have no idea how to do this particular question because the parameters change partway through. Does anyone have any ideas? I'll use U as the partial derivative of U with respect to s.
Let W(s,t) = F(u(s,t),v(s,t) where
u(1,0) = -4
u(1,0) = 7
u(1,0) = -1
v(1,0) = 4
v(1,0) = -5
v(1,0) = -2
F(-4,4) = 6
F(-4,4) = -6

Find W(1,0) and W(1,0)

2007-09-16 09:02:10 · 1 answers · asked by razorj06 2 in Science & Mathematics Mathematics

1 answers

Actually, there is a standard notation for subscripts, which is to write them after an underscore, so for instance ∂W/∂s = W_s. This should help you in the future.

Anyway, this is just an application of the chain rule:

W=F(u, v)

∂W/∂s = ∂F/∂u * ∂u/∂s + ∂F/∂v * ∂v/∂s

So W_s(1, 0) = F_u(u(1, 0), v(1, 0)) * u_s(1, 0) + F_v(u(1, 0), v(1, 0)) * v_s(1, 0)

Now just plug in the known values:

F_u(-4, 4) * u_s(1, 0) + F_v(-4, 4) * v_s(1, 0)
6*7 + (-6)*(-5)
72

The calculation for W_t is similar:

∂W/∂t = ∂F/∂u * ∂u/∂t + ∂F/∂v * ∂v/∂t

W_t(1, 0) = F_u(u(1, 0), v(1, 0)) * u_t(1, 0) + F_v(u(1, 0), v(1, 0)) * v_t(1, 0)

F_u(-4, 4) * u_t(1, 0) + F_v(-4, 4) * v_t(1, 0)
6*(-1) + (-6)*(-2)
6

And we are done.

2007-09-16 15:18:03 · answer #1 · answered by Pascal 7 · 0 0

fedest.com, questions and answers