Question

Let w(s,t)=F(u(s,t),v(s,t)),where F,u and v are differentiable,u(1,0)=2

Answer 1

Answer:

$ws(1,0)=52$

$wt(1,0)=34$

Step-by-step explanation:

u                              v

$u(1, 0) = 2..............v(1, 0) = 3$

$us(1, 0) = -2............vs(1, 0) = 5$

$ut(1, 0) = 6............vt(1, 0) = 4$

$Fu(2, 3) = -1.............Fv(2, 3) = 10$

To find $w_{s}$ :

we have to use the above equation, which is subscription notation

w(s, t) = F(u(s, t), v(s, t))

(1, 0) = ((u(1, 0), v(1, 0)), (u(1, 0), v(1, 0))) · ((1, 0), (1, 0))

           = ((2, 3), (2, 3)) · (−2, 5)

           = $(-1, 10) * (-2, 5)$  expand

           =$(2)+(50)$

           =$52$

To find $w_{t}$ :

 wt(1, 0) = ((u(1, 0), v(1, 0)), (u(1, 0), v(1, 0))) · ((1, 0), (1, 0))

             = ((2, 3), (2, 3)) · (6, 4)

             =$(-1, 10) * (6, 4)$   expand

             =$(-6)+(40)$

             =$34$