Use the general chain rule to find DH (1,-1) given G(U)=G(u, v) = and H(U)= F(G(U)). /u²+3v² +2 F(X) = F(x, y, z) = [ - x² + y² + 2z² x² - y² '],

Q: From the previous page: the function f(x) = e*(x² + x – 1) has derivatives f'(x) = e*(x² + 3x),…

A: Consider the following function: fx=exx2+x-1f'x=exx2+3x Consider the part (e): Linear approximation…

Q: (x+1)+-y² Suppose g(x, y) = {(x+1)++y² ' (-1, if (x, y) + (0,1) if (x, y) = (0,1) Find g,(0,1) and…

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Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A: our objective is to find the required derivative

Q: Consider the function g(x, y) = x² + xy + y² (1 + 1/2t, 2 + V3/2t), use the (a) Given the line l(t)…

A: Given,              g(x, y)=x2+xy+y2

Q: Suppose z = x² sin y, x = s² + 3t², y = 6st. Əz Əz A. Use the chain rule to find oz and 0 as…

A: Suppose .(A) By using chain rule to find  as functions of .(B) To find the numerical values of  when…

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Find the first order partial derivatives of: (a) g(x1, x2) = (3x1 + 2x2) 5. Ans: f1=? f2=? (b)…

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Q: The function z(x, y) obeys, = -2e Which of the follow represents a valid first step for finding u(x,…

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Q: = 0. c) y(0) = 1, y'(0) = 0, y"(0) = -1. Is the set of functions linearly independent or linearly…

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Q: Consider the function - f(x, y) = 2x² + xy² − 6xy + 5x +2. (a) Show that (1,3) is a stationary point…

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Q: Let f(x, y, 2) =x² + 3r°y? + 2°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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Q: Let f(x, y) = (x° + ay´, xʻy°, 2x+by), g(u,v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: f(x,y)=(x3+ay2,x2y3,2x+by)g(u,v,w)=(3u2+bv2+w3,uvw)To Find: Derivative of f(g(u,v,w)) using the…

Q: L(x) = b) Use the linearization to approximate 125.1 ~

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Q: Let h(æ, y) = f(x)g(y) + (9(y))² and suppose that f(1) = 5, f'(1) = 3, g(2) = 8, g'(2) = 10. Then…

A: Given function is - h(x,y) = f(x) g(y) + g(y)2             ............................(1)We have to…

Q: Find fyx for f(x,y)=exln(y)

A: Given : fx,y = exlny

Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: Consider f(x, y) = xy(²-x²) x² + y² 0 if (x, y) = (0,0) if (x, y) = (0,0) . Show that fay(0,0) = 1…

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Q: Consider the function: f (x,y) = 2x² - 4x - xy² + 2y² - 3. Explain and then use the chain rule for…

A: The given problem is to find the small changes to estimate the change in the function f(x,y) that…

Q: say f(3)=5, f'(3)=-2 and let g(x) =xf(x/2) find the linearization of g(x) at x=6

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Q: Find fy(x,y) if f(x,y)= (x+y4) 5. fxy(x,y) =

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