Let w(z, y, z) = 1 + y² + z?, where z = 3', y = Int, and z = = et. Find I using the Chain Rule.

Q: Use the Chain Rule to find Əz/əs and əz/ət. z = x°y', x= s cos(t), y = s sin(t) az as %3D az %3D at

A: Total derivative

Q: let y= (x + sin(x)) Find gix), fcx) e deriv ative f(x) = so that y=(fog)(compute usin Chain Rule ニ

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Q: Use the Chain Rule to find ôz/ðs and dz/ðt. z = e" cos(0), r= st, Vs4 + t4 Əz as az at II

A: Given

Q: 3.2= e'-ry ; I=t3 and y = t° %3D

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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: 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: Find the Green's function for with homogenous Dirichlet b conditions in the half cylindr < R, 0 < <…

A: The impulse response of an inhomogeneous linear differential operator defined on a domain with…

Q: Use the Chain Rule to find az/as and az/at. z = e" cos(0), r = st, 0 = V s8 + t8 az as az at

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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: w In(x2 + y2 +z?), x = ue" sin u, y = ue" cos u and z ue", using chain rule at the point (u, v) =…

A: Given w=lnx2+y2+z2x=uevsinuy=uevcosuz=uev

Q: Use the Chain Rule to find aw at w = xycos z; x = t6, y = t³, z = arccost

A: The given functions are w=xycos z ; x=t6 , y= t3 , z= cos-1t. To Evaluate: ∂w∂t. As per policy, we…

Q: Let X, Y be jointly Gaussian, standard, and Cov (X,Y) = y. Find pdf of Z = X +

A: Answer:-  Given that, X and Y have jointly Gaussian distribution.

Q: dz Use chain rule to find at (u, v) = (1, 1) if dv z = z sin(y² – z + 1)4), e = 3u – v², y = vº.

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Q: Let u = cos(r + y), x = 2st +t and y = t – 2s. Use the chain rule theorem to compute du for du and…

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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: 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…

Q: Use the Chain Rule to find əz/əs and əz/ət. z = (x - y)5, x = s?t, y = st2 az as az at

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Q: Use the chain rule to find dw/dt, where w=x^5y^4+y^3z^2, x=e^t y=e^tsint, z=e^tcost First the…

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Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

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Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

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Q: Use the Chain Rule to find dz/əs and dz/at. z = tan(u/v), u = 8s + 3t, V = 3s 8t az as az Ət II

A: Given data: *z=tan(uv) *u=8s+3t and v=3s-8t The partial derivative of z with respect to s is given…

Q: Use the Chain Rule to find dz/ðs and əz/ət. z = tan(u/v), u = 5s + 8t, v = 8s – 5t %3D az %3D as az…

A: We have to use chain rule to find the partial derivatives of z.

Q: 2. In A ABC, X is the centroid. A A If CW = 15, find cx and XW. W, B. If BX = 8, find BY and XY.

A: we know that  centroid is located 23 of the distance from the vertex along the segment that connects…

Q: u,v) = ve*tv, and z(u,v) = (u+v)cos v?. OG nd and by using multivariable Chain Rule method. du u=1

A: Given: Gx, y, z=e2x+y+3zxu, v=u lnu+vyu, v=veu+vzu, v=u+v cos v2  To Find: To find  ∂G∂uu=1v=0  and…

Q: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

Q: Given: f(x,y) = 2x²y³ and the points (1,2) and (1.1, 2.05) a.) Find f(1,2) and f(1.1,2.05). Then…

A: Here we want to find ∆Z using the function values and total differential.

Q: Use the Chain Rule to find az/ðs and ôz/dt. z = arcsin(x – y), x = s² + t?, y = 2 - 2st as az at II

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Q: Suppose that a, b, c, and d are constants such that ad- be # 0, and let m and n be arbitrary real…

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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: By using the chain rule for partial differentiation we will find the value of it.

Q: | Let u = x*y + y°23 where x = rse', y = rs²e=t, = 2, 8 = 1 and t = 0, by using Chain Rule. p2 Sint.…

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Q: Use Chain Rule to find ds given w = Vr² – 2y + z² and r = cos (st), y = -2s Int and z = s –

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Q: Let u(x,y,t)=(1/t)exp[-(x²+y²)/4t] where exp denotes e to a function. Show that u(x,y,t) satisfies…

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Q: Express dw/ar and aw/as as functions of r and s using chain rule w = In(x² + y² + z²), x = re sin r,…

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Q: Let {yk } be the DFT of {x; }, where x = [0, –1, 0, 1] y3 = O i -1 -i 1

A: Here, x0=0, x1=−1, x2=0 and x3=1 We have to find y3 Now, y3 is given by…

Q: Let z = f(x, y) where g = e° cos t and y = e sin t. Use the Chain Rule to show: az, a z = e

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Q: Consider F(x, y, z)=e-2 yi-y³/²zx²j+ln(22)k and calculate the divergence of F.

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

Q: Eveluake F.dv wlere flaiy,z) where the segnent on Cis (-',2,0) to (3,0,1)

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Q: Use the Chain Rule to find az/ds and az/ôt. z = tan(u/v), u = 3s + 6t, v = 6s - 3t az as az at II

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Q: Use the Chain Rule to find zz and zy given sin(u) tan(v), u = 3x + y, and v = x – y. %3D

A: Given z = sin(u) tan(v)where u = 3x + yv = x - y

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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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: Express dw/dr and dw/as as functions of r and s using chain rule w = In(x + y + z*), x = re sin r, y…

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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: find du/dt for u=4ysin(x)+xze^xy^2 and x=3s+t, y=ln(s+t), z=cos(st)

A: The objective is to find  dudt, where u=4ysin(x)+xzexy2, x=3s+t, y=ln(s+t), and z=cos(st)

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 = f(x, y) where g = e° cos t and y = e° sin t. Use the Chain Rule to show: z = e

A: Let z = f(x, y) where x = es cos t and y = es  sin t. We will be using the chain rule to show,…

Q: Use the Chain Rule to find ôz/ds and ôz/ðt. z = tan(u/v), u = 5s + 9t, V = 9s – 5t az as az at

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Q: Use the Chain Rule to find ôz/ðs and dz/dt. z = tan(u/v), u = 3s + 6t, v = 6s – 3t dz %3D as Ot

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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: 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…