Question

Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies. u(1, −9) = 3 v(1, −9) = 0 us(1, −9) = 9 vs(1, −9) = −6 ut(1, −9) = 4 vt(1, −9) = 7 Fu(3, 0) = −2 Fv(3, 0) = −4 Find Ws(1, −9) and Wt(1, −9).

Answer 1

Answer:

$W_{s} =6\\W_{t} =-36$

Step-by-step explanation:

               u                                       v

$u(1, -9) = 3.......................v(1, -9) = 0$

$us(1, -9) = 9....................vs(1, -9) = -6$

$ut(1, -9) = 4.......................vt(1, -9) = 7$

$Fu(3, 0) = -2.....................Fv(3, 0) = -4$

To find $W_{s}$

Now we can apply the above expression

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

(1,-9)=((u(1, -9), v(1, -9)), (u(1, -9), v(1, -9))) · ((1, -9), (1, -9))

         =($F_{u}$(3, 0), $F_{v}$(3, 0)) · (9, -6)

        $=(-2,-4).(9,-6)\\=(-18)+(24)\\=6$

To find $W_{t}$:

(1,-9)=((u(1, -9), v(1, -9)), (u(1, -9), v(1, -9))) · ((1, -9), (1, -9))

          = ($F_{u}$(3, 0), $F_{v}$(3, 0)) · (4, 7)

          $=(-2,-4).(4,7)\\=(-8)+(-28)\\=-36$