Question

let w(s,t)=F(u(s,t),v(s,t)),where F,u and v are differentiable,u(1,0)=2 uₛ=(1,0)=-2,uₜ=(1,0)=6,v(1,0)=3,vₛ(1,0)=5,vₜ(1,0)=4,Fᵤ(2,3)=-1, Fᵥ(2,3)=10 Find wₛ(1,0) AND wₜ(1,0)

Answer 1

To find wₛ(1,0) and wₜ(1,0), we need to evaluate the partial derivatives of w(s, t) with respect to s and t. The value of wₛ(1,0) is -2Fₛ(2,3) - 1, and the value of wₜ(1,0) is 6Fₜ(2,3) + 10.

Step-by-step explanation:

To find wₛ(1,0) and wₜ(1,0), we need to evaluate the partial derivatives of w(s, t) with respect to s and t. Let's start with wₛ(1,0):

wₛ(1,0) = Fₛ(u(1,0), v(1,0)) * uₛ(1,0) + Fᵤ(u(1,0), v(1,0))

Substituting the given values:

wₛ(1,0) = Fₛ(2,3) * (-2) + (-1) = -2Fₛ(2,3) - 1

Similarly, to find wₜ(1,0):

wₜ(1,0) = Fₜ(u(1,0), v(1,0)) * uₜ(1,0) + Fᵥ(u(1,0), v(1,0))

wₜ(1,0) = Fₜ(2,3) * 6 + 10 = 6Fₜ(2,3) + 10