Use the chain rule to find dW/ds & dW/dt

[MarkSA]

Hello.. I'm really confused about how to work this problem.

Q: Let W(s,t) = F(u(s,t),v(s,t)), where F, u, and v are differentiable. u(1,0) = 2, u[sub:2mu4zwdr]s[/sub:2mu4zwdr](1,0) = -2, u[sub:2mu4zwdr]t[/sub:2mu4zwdr](1,0) = 6, v(1,0) = 3, v[sub:2mu4zwdr]s[/sub:2mu4zwdr](1,0) = 5, v[sub:2mu4zwdr]t[/sub:2mu4zwdr](1,0) = 4, F[sub:2mu4zwdr]u[/sub:2mu4zwdr](2,3) = -1, and F[sub:2mu4zwdr]v[/sub:2mu4zwdr](2,3) = 10.

Find W[sub:2mu4zwdr]s[/sub:2mu4zwdr](1,0) and W[sub:2mu4zwdr]t[/sub:2mu4zwdr](1,0)

I'm really lost. I feel comfortable using the chain rule for functions of a single variable, but I'm having trouble seeing what is going on and what procedures to use for functions of multi-variables... appreciate any help you can provide.

 

[Deleted member 4993]

Hello.. I'm really confused about how to work this problem.

Q: Let W(s,t) = F(u(s,t),v(s,t)), where F, u, and v are differentiable. u(1,0) = 2, u[sub:2ie2byn4]s[/sub:2ie2byn4](1,0) = -2, u[sub:2ie2byn4]t[/sub:2ie2byn4](1,0) = 6, v(1,0) = 3, v[sub:2ie2byn4]s[/sub:2ie2byn4](1,0) = 5, v[sub:2ie2byn4]t[/sub:2ie2byn4](1,0) = 4, F[sub:2ie2byn4]u[/sub:2ie2byn4](2,3) = -1, and F[sub:2ie2byn4]v[/sub:2ie2byn4](2,3) = 10.

Find W[sub:2ie2byn4]s[/sub:2ie2byn4](1,0) and W[sub:2ie2byn4]t[/sub:2ie2byn4](1,0)

I'm really lost. I feel comfortable using the chain rule for functions of a single variable, but I'm having trouble seeing what is going on and what procedures to use for functions of multi-variables... appreciate any help you can provide.

\(\displaystyle \frac{\delta W}{\delta s} \, = \, \frac{\delta F}{\delta u}\cdot \frac{\delta u}{\delta s} \, + \, \frac{\delta F}{\delta v}\cdot \frac{\delta v}{\delta s}\)

and so on...