Suppose that w = f(x, y, z), x = e"s, y = s², and z = r cos(rs). (a) Use the Chain Rule to write down formulas for and dr ds (b) Given that wr(1,4,0) = 3, w,(1,4,0) = 2, and wz(1,4, 0) = -3, find the value of and when dr ds r = 0 and s = 2.

Q: dw Use an appropriate form of the chain rule to find dt w = In(82? – 4y + 5z³); = t, y = tỉ, z = t-2…

A: w=ln8x2-4y+5z3x=t12y=t23z=t-2The chain rule says dwdt=dwdxdxdt+dwdydydt+dwdzdzdt

Q: 2. If T = u? + v²,u = x+ y+z,v= ryz. Using the chain rule to find and when r = 1, y = 2, z = 3. Draw…

A: Given that: T=u2+v2u=x+y+zv=xyzx=1, y=2, z=3

Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = √u and u = x3

A: Recall the chain rule of differentiation:

Q: What technique should you use to solve the ODE that arises from the Euler's equation associated with…

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: EXAMPLE 2: dz 1 Given that z = x+y,where x = and y 2r. Find by: dt 1 a. Substituting x= and y = 2r'…

A: From the given problem:   z=x2+y2 ; x=1t2 ; y=2t3 a). Now, substitute x=1t2 ; y=2t3 in z=x2+y2 .…

Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

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Q: 1. Use the Chain Rule to find dy in terms of r. dr а у — (и—2)3 and и- 2x +1 b. y = Jū and u= 5z2 –…

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Q: dw Use an appropriate form of the chain rule to find dt w = In(10x² – 4y + 5z³); c = t', y = tỉ, z =…

A: From the given function: w=ln10x2-4y+5z3 ; x=t12 ; y=t23 ; z=t-2 As we know that: The Power law:…

Q: dw Use the Chain Rule to find dt w = 7x°y°z,x = 2t, y = cos(4t), z = tsint %3D 7xy°(12yz -…

A: see 2nd and 3rd step.aa

Q: Q1) Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3, by using the Chain Rule dt

A:

Q: Suppose z = x2 sin y, x = 2s? + 3t2, y = 6st. A. Use the chain rule to find and as functions of x,…

A: (A) ∂z∂s=∂z∂x.∂x∂s. Take derivative of z=x2siny w.r.t x : ∂z∂x=2xsiny=4s2+6t2sin6st. And, ∂x∂s=4s.…

Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

A: Express dw/dt as a function of t by using the Chain Rule. Use the sum rule and split the bracket.…

Q: 7) Suppose w=rt+rs' and r= tan-' (2x² +3y), s=x²y' +3y and t = x²y² .Use the chain rule (from…

A: Given w=r2t+rs3r=tan−1(2x2+3y)s=x2y3+3yt=x2y2

Q: Suppose z = x² sin y, x = 2s2 + 3t2, y = 4st. dz and A. Use the chain rule to find ds as functions…

A: Given: z=x2siny x=2s2+3t2 y=4st To find: Using chain rule, ∂z∂s and ∂z∂t ∂z∂s1,-2 and ∂z∂t1,-2

Q: find the linearization at x = a: y = ex ln x, a = 1

A: fx=ex lnx,  a=1 Differentiating with respect to x, we get f'x=dexdx·lnx+dlnxdx·ex=ex lnx+1xex Now,…

Q: Let F(x, y, z) = (2x cos(y), e² – x² sin(y), ye²). (a) If possible, find all potential functions for…

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Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = u3 and u = √x

A: Given: ,and . Find out by using the chain rule.

Q: Use the Chain Rule to find az/as and az/at. sin(0) cos(p), 0 = st7, p = s³t əz t³cos(p) cos(0) —…

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Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: 7-10 Use an appropriate form of the chain rule to find dw/dt. w = 5 cos xy - sin xz; x = 1/t, y = t,…

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Q: Use chain rule to find given x² + 2y² + z² and x os (st), y %3D Cos

A: Solve the following

Q: Let f(x, y) = 2x - 5y, r(1) = (cos(t), sin(t)). Use the Chain Rule to calculate f (r(t)) at the…

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Q: Suppose z = x² sin y, x = 3s² +lt², y= 2st. A. Use the chain rule to find and as functions of x, y,…

A: Consider:z=x2sin y, x=3s2+t2, y=2st. A1) Find ∂z∂s. Apply chain rule ∂z∂s=∂z∂x·∂x∂s+ ∂z∂y·∂y∂s Find…

Q: az and as az Use the chain rule to find at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az at

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Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: ди and ди ди Q3. If u = e"" sin p, p= sin x, q = z' In y, r=1/z, use chain rule to find

A: Find your answer below

Q: 19. Let f(x, y, z) = + sin(3z) + e"-2". Find the rate at which f is changing at (2, 4,0) in the…

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Q: 2. Use the Chain Rule to find for z = e¤/y where x = st and y = s2 +t

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Q: Suppose z = x2 sin y, x = 3s2 + 2t2, y = 4st. A. Use the chain rule to find az and as az as…

A: We will solve the problem applying chain rule.

Q: Q1) suppose that W= x2+y2+z² and x cos 0, y = sin0, z = tan 0 ,use the chain rule to find de when 0

A: We have, W=x2+y2+z2 and x=cosθ, y=sinθ, z=tanθ  We have to find, dwdθ=? at θ=π4

Q: Suppose that w = f(x,y, z), x = h(s), y= g(s, t), z= k(s,t) and all the conditions required for the…

A: Given that w=fx,y,z, x=hs, y=gs,t and z=ks,t. We have to compute ∂w∂t by using chain rule. Since, by…

Q: Suppose z = a? sin y, x = 2s² + 3t², y = 4st. A. Use the chain rule to find az and dz as functions…

A: Given : z=x2sin y x=2s2+3t2y=4st To evaluate: ∂z∂t,∂z∂s

Q: Suppose that u = x²y, where x = r cos 0 and y = r sin 0. du Compute the partial derivatives du and…

A: Given that u=x2y  ….(1) where x=rcosθ  and y=rsinθ Differentiating (1) partially with respect to 'r'…

Q: _Suppose w =+, x = cos² t, y = sin? t, z = ; dw Evaluate at t = 3, by using the Chain Rule dt

A:

Q: If z = sin(x/y) and x = ln (u) and y = v^4, find the partial derivatives of z with respect to u and…

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Q: If z = f(x,y) = tan x =t cose and y =t sin@. Use the Chain Rule method to find y as functions of t…

A: Given that z=f(x,y)=tan-1xy Where x=tcosθ,y=tsinθ Substituting, the values,…

Q: Find the first partial derivatives of the function. u(r, 6) = 4 sin(r cos(6)) %3D 4,(r, 6) %3D Ugr,…

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Q: 2 Let z=x ·sin(y) 2 X=S •t y= st. dz Compute & in two ways: (i) Using the chain rule and S ô t (ii)…

A: Given that , z=x2siny where x=s2t , y=st find ∂z∂s , ∂z∂t

Q: Suppose z = x sin y, x =. 3s2 + 2t2, y = 4st. az A. Use the chain rule to find az and as as…

A: Chain rule

Q: Let w f(t,0) where t and 0 are functions ofr and s, %3D dw is equal to Or then according to the…

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Q: Suppose z = x² sin y, x = -s² – 21² , y = 8st. dz A. Use the chain rule to find and * as functions…

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Q: b- Use Chain Rule to compute w = 2y e* - Inz } əw at x = ln(t² + 1), at (t) equal to (1) for: y =…

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Q: Let z = f(x, y) and suppose x = 2u – 3v and y = 5u + 6v. Use the chain rule to express dz in terms…

A: x=2u-3vy=5u+6v Now we apply the chain rule  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u Take derivative of x  and y…

Q: Let z = g(x, y) = x² + xy³ -y - 6x - 2y +4, where x = r cos (8) and y = r sin(8). дz Use the chain…

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Q: Let c(t) Use the chain rule to compute (foc)'(t). (cos(t), sin(t), t²) and f(x, y, z) = x² + y² +…

A: The objective is to find the derivative.

Q: (a) Let F z sin y, where r(s,t) = st and y(s, t) = st. Use the chain rule to find %3D %3! OF

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Q: Q1) Suppose w =÷+ ?, x = cos² t, y = sin² t, z = ; Evaluate dw at t = 3, by using the Chain Rule dt

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Q: Use the chain rule to find ∂w/∂t given w =√ x^2 + y^2 + z^2 and x = cos(st), y = −2s ln(t) and z = s…

A: Solution:Given      w=x2+y2+z2x = cos(st), y = −2s ln(t) and z = s − 3t.To find…