Let f(x, y, z) = x³e" Vz² + 5 and let x = rt², y = r2t², and z = sin(t) cos(r). (a) Draw a tree diagram for the chain rule. af (b) Find a formula for дt af (c) Compute дt

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

A: Given- w=x2+y2, x=cost, y=sint and t=π To Find- The value of dwdt as a function of t, both by using…

Q: tan (X) where : Let z=f(x,y) = (10 + 23x)y" where : 13 - e (t – 1) + tan'(t) , and y= (2- t) e'-…

A: Here, the given functions are: z=f(x,y)=(10+23x)ytan xx=13-e2e(t-1)+tan-1(t)y=(2-t)et-13(t-1)

Q: M Using the chain rule and/or product rule and take the denvative of yit) with respect to time, t b)…

A: We are entitled to solve one question at a time and up to 3 sub-parts only. Please post other…

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: Q12- Suppose that we, x= 3r+s, y= 3r-s, z= r²s Use appropriate forms of the chain rule to find dw dw…

A: To evaluate by using the appropriate form of the chain rule.

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: az az Use the chain rule to find and as at Z = In(3x + 5y), x = s sin(t), y = t cos(s) az az at

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

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Q: 17-22 Use appropriate forms of the chain rule to find ðz/du and Əz/dv. 17. z = &x?y – 2r + 3y; x=…

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Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: Əz Q3.If Z= f(x,y) = 4 e In(y), and x = ln (u cosv), y = u sinv, use chain rule to find : E * ди Q4.…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: az az and at as Use the chain rule to find z = tan-(x + y°), x = s In(t), y = tes az as az at

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Q: dw as a function of t, both by using the chain rule and by expressing w in terms of t and…

A: Given query is to find the derivative of the expression.

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

A: Consider the following equation: w=x2+y2 Substitute x=cost+sint and y=cost-sint in the above…

Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 2. z = In(2x² + y); x = /i, y = 12/3…

A: Given: z=ln(2x2+y);  x=t , y=t2/3To find:dzdt=??

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: Please solve. Thank you

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Q: Let z = g (x, y) = x³ + xy³ + y4 - 6x - 2y + 4, where x = r cos (0) and y дz Use the chain rule to…

A: We will use chain rule to find the derivative

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

A: A) The function x is differentiated as, x=cost⇒dxdt=-sint The function y is differentiated as,…

Q: əz ди Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), yusin v, use chain rule to find : (x²) dr du…

A: 3. Given Z=fx, y=4 ex lny and x=lnu cosv, y= u sinv   To Find: ∂Z∂u and ∂Z∂v

Q: Let f (x, y) = 3x – 2²y. x = -t, y = s + 2t dz dz Use an appropriate chain rule (involving , , etc.)…

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Q: Let f(x, y) xy, x = 1- Vt, and y = 1+ Vt. Find df using the chain rule. dt

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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: Suppose z x'y' where x-st and y -t -s. Use the chain rule to determine as and a) -2xy't-4yx's;-…

A: The given multivariable function is: z=x2y2 ,       where x=st     and     y=t2-s2

Q: B. Differentiate the following using Chain Rule. 3.f (2) = (322- 플 + z)" (3=² – +=

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Q: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

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

A: w=x2+y2, x=cost, y=sint, t=π, We have to a) express dWdt as a function of t, both by using the Chain…

Q: (a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by…

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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: We find dw/dt using chain rule. Here plug x = cos t, y = sin t, z = 4sqrt(t) and simplify.

Q: 1. Use the Chain Rule to find y = (u-2)³ and u = da in terms of x. 1 2x+1

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

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Q: Əz 1 Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), yusin v, use chain rule to find : 201 ди and az

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Q: Suppose z = x´ sin y, x = 2s2 + 3t2, y = 6st. A. Use the chain rule to find z and as functions of x,…

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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: 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: Q2-By using Chain Rule, find au/ax, du/dy, du/dz at (x, y, z) = (√√3,2,1) U= p-q q-r p=x+y+z…

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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: əz Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), y = u sin v, use chain rule to find : 2 ди Q4.…

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Q: Consider the functions z = -2e" In y, x = In (u cos v), and y = u sin v. dz dz (a) Express and du as…

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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: Exercise (4.5) Recall that d 1, x > 0 (1xl) = dx -1, x< 0 d Use this result and the chain rule to…

A: We have to find derivative

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: 13. Use the chain rule, in Leibniz notation, to find dx dy at the given value of x. а. у %3D Зи? —…

A: We are solving the first three subparts and for the next subparts post the question againand also…

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: 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: az az Use the chain rule to find and əs at z = tan(x° + y°), x = s In(t), y = tes az as az at II II

A: