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Q: 1. Given w = x²y³z+x*yz³, x = cos(4t),y = sin(5t),z = In(t). Write the tree diagram for . Then,…

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

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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 .…

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A: Given: The expression 2cosϕsinϕ+cos2ϕcscϕ, To simplify: The given expression in term of one…

Q: 3. Find dy, where; a) cos(ry) - e 2 elx+y). b) ė?+ Ptany =4, u= xlax (use chain rule)

A: We have to find the derivative

Q: 2. If z y where z= s cos t and y=s sin t, find az/ôs and az/at.

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Q: If z= r +y, I= e' cos(s) and y= e' sin(s), then %3D 8z as at (t, s) = (1,0) is O-2e O 4e O 2e? 2e

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Q: Find Oz! ôu and dzlôv for z= 4e" In(y), x In(u cos(v), y=u sin(v) at the point (u,v)= (2, 7 / 4).…

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Q: An ODE is said to be stable if every abitrary constanst on its solution, such as C1 and C2 for…

A: A function fx is said to be stable in terms of differential equation solutions if any other solution…

Q: az əz 1. ax' dy If z = In(e* + e"), show that %3D %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: 4. Calculate leme/) at (z,y) = (a, 4). sin(z/g) ey2/2 A ev2/2 B 4

A: Here we have to calculate ∂∂xesin(x/y)=? at (x,y)=(π,4)

Q: et u = e Sin P= sin sc Lind su using chain Rule

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Q: .....E E 行 az Əz and at Use the chain rule to find as z = In(3x + 5y), x = s sin(t), y = t cos(s) az…

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Q: Suppose w = In(8x² + 2y² + 3z²), ¤= 9 cos(t) , y = 9 sin(t) , and z = 8Vt. Compute dw/dt in two…

A: The partial derivative of a multivariable function with respect to any of the variables can be…

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Q: The solution of (1+y?)+(t- elan-ly. dy =0 is: dt %3D Select one: a. t = ce2tan-ly+ 2 %3D O b. 1 C…

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A: Given: Wt is a standard Brownian motion  0&lt;s&lt;t&lt;infinity

Q: az az and as Use the chain rule to find at sin(0) Z = r = st, 0 = s6 + t6 6sºcos 6 + ,6 sin s° + t°…

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Q: Consider the following homogeneous linear DE: y" + 8a y' + 4 y(t) = 0 where a is a constant.…

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Q: Let C, be the rectangle with vertices (0,0). (1,0) (0,2) and (1,2) oriented counterclockwise. Find J…

A: Green's theorem problem....

Q: Now consider the following nonhomogeneous linear DE; y" + 16 y = 2 sin(2rwt) For what value(s) of w…

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Q: Ex: If w cos(uv), u = = xyz, y = π 4(x²+y²)' aw find at point (1, 1, 1). əx

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Q: Suppose that w = x² + y? + z², x = cos 0, y = sin 0, z = tan 6. Use the chain rule to find dw when 0…

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Q: Suppose z = a? sin y, x = -s? – 5t², y = 8st. az and A. Use the chain rule to find as functions of…

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Q: The function z = cos 0, y = sin³ 0 where 0 < 0 < 27. Use the x2 Vy is defined on the astroid x = dz…

A: The chain rule is stated as follows:

Q: 3. 2.m (ris, t)= e cos (25) y= h(ris, t)- e sini (s) %3D + そ人メ+ (てん「以) =1 け! ne Use chain rule to…

A: Given, u=fx,y,z=x3+xyz+z2x=gr,s,t=e2rcossy=hr,s,t=e2rsinsz=mr,s,t=ercos2s To find: ∂u∂s Formulas…

Q: 3. Given that z= (u, v), where u 2r cos y and vz sin y. Find and Hence, show that Dy

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Q: . Let w- e*² <in Cyz)- e Yz cor Cxz) Find - W X

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Q: An ODE is said to be stable if every abitrary constanst on its solution, such as C1 and C2 for…

A: Given  yh = C1*eat + C2ebt

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

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Q: For the IVP: (1-4) cos ty"-In(r-1)y+VT+5y=e, y(2) =1, y(2) = 1

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Q: 3. Given that z = e" cos (), u = 4e2" – sin 2y, v = e" + n tan r. COS - Use chain rule to find dz/ðx…

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Q: dz a²z and 1 a) Find- Usin chain rule. If z = e*y – Sin xy, x=-, y=t? дх ду dt

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Q: 3. Let V = e" cos(qr), with p= r In(ryz), q = z cos(ry) and r = 2 tan-(y). Ae when r= y = 2 = 1. By…

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Q: -a cos y + ze-1/(1+y²), then If f(x, y, z) = el- of ?x ; |(1,0,п) = fæ (1, 0, 7).] (Show solution.)…

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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: L[t cos 2t

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Q: ,3 Let w = x'y cos(2z). Find the following. dw (a) (x, y, z) = (b) (x, y, z) = ду (c) (x, y, z) = dz

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Q: The indicated Turi Is a solution of th1e given d merentiai equation. Ose iula (5) Tn Section 4.2…

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Q: If w = Vr + y² + zª where r= sin(0), y = cos(@) and z = Use the Chain Rule to find tan(@). dw when…

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Q: Use the Chain Rule to find az/as and az/at. (Enter your answer only in terms of s and t.) z = sin(0)…

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Q: If (х, у) %3D х" у"is an integratingfactor of the the DE. (1+ 3ху)dx + (ху-1 +x?)dy %3 0 Then, the…

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Q: 11 z- CCW -dz, z2 - z de. c:|2- = sec(u), <ý<.cv Question 11) Find I =

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Q: 2 tan-1(y). x In(xyz), q ƏV when x = y = % = 1. ду Let V = eP cos(qr), with p = z cos(TY) and r = By…

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Q: . Let z = x2 – x*y where x = r sin 0 and y = r cos 0. az and ae az Use the chain rule to find ar…

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