1. The problem statement, all variables and given/known data Let f:R2−>R be a differentiable function at any point, and g be the function g:R3−>R2defined by: g(u,v,w)=(g1,g2)=(u2+v2+w2,u+v+w) consider the function h=fog and prove that ||∇h||^2 = 4(∂f/∂x)^2*g1 + 4(∂f/∂x)(∂f/∂y)*g2 + 3(∂f/∂y)^2. 3. The attempt at a solution H=fog=f(g1,g2) ∇h=∇(fog)=<∇f(g1,g2),∇g(u,v,w)> (dot product) ∇g(u,v,w)=(2u+2v+2w, 3) ∇f(x,y)=(∂f/∂x)+(∂f/∂y) evaluated at g1 and g2 respectively. <∇f(g1,g2),∇g(u,v,w)>=(∂f/∂x)∇g1+(∂f/∂y)∇g2=∇h I stopped here because looking ahead, I can see that I will ultimately be wrong here. I can see that (∂f/∂x)^2 + (∂f/∂x)(∂f/∂y) + (∂f/∂y)^2 will come from squaring my answer for ∇h., the 3 in front of (∂f/∂y)^2 is the same as ∇g2, and the 4 in front of (∂f/∂x)^2 may come from factoring out the 2 from ∇g2 and then squaring it. Any help? I would just like to know where in my process I went wrong and what I should be doing for the following step. Thank you!