By using Chain Rule, find au/əx, du/dy, du/dz at (x, y, z)=(√√3, 2, 1) p-q u= q-r p = x+y+z q=x-y+z, r = x+y-z }
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- Find ƒyxyz if ƒ(x, y, z) = 1 - 2xy2z + x2y.express ∂w ∂u and ∂w ∂v using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate ∂w ∂u and ∂w ∂v at the point (u,v)=− 2/3 ,2.Using the chain rule, find df/dt in terms of t if, f(x,y)=xsin(y) and x = 5*t, y = t^2
- Find the linearization of y=√x at a=49. Then use your linearization to approximate √56. Show workexpress ∂w ∂u and ∂w ∂v using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate ∂w ∂u and ∂w ∂v at the point (u,v)= 1 2,−2.Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by W(f1,f2)=e2xW(f1,f2)=e2x. Are the functions that you found linearly independent on (−∞,∞)(−∞,∞)? How do you know?