Use the Chain Rule to find z, and zį a) z = Vre"y, x = 1+ st , y = s² – t²

Q: 4. z = tan-'(y/x), x = e', y = 1 - et

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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: Integrate F(r)= [e2*, e²y,e²²] along the helix that cuts the z-axis at c.

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Q: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

Q: dw dw and du For the functions w =xy + yz + xz, x=u + v, y =u - v, and z= uv, express using the…

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Q: Find S, F· dř tor F = -5yỉ + 4x} – 4zk if C is the helix x = cos t, y = sin t, z = t, for 0 < t <…

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Q: Use the Chain Rule to find Əz/əs and əz/Ət. z = e' cos(0), r= st, 0 56 + t6 Əz as ze at %3D II II

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Q: use the Chain Rule to calculate f (r(t)). 8(x, y, z, w) = x + 2y + 3z + 5w, r(1) = (12, 13, 1, 1–2).…

A: Given, g(x,y,z,w)=x+2y+3xz+5w, r(t)=t2,t3,t,t-2, t=1 To find ddtg(r(t)).

Q: tu+v dt In(t) f(u, v) = u-1 fy Find using the chain rule u = x +y³, v= 3y- 3xs

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Q: Consider the functions f(x, y, z, t) z?, t?) and g(u, v) = (uv, u +v, u – v). Use the chain rule to…

A: I have solved in general and also using chain rule. Composition  of several variable functions:  Let…

Q: Use the chain rule to find , where w = x*y* + y? z³, æ = e*, y = e* sin t, z = e' cos t First the…

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Q: Use the Chain Rule to find dz/ds and dz/dt. z = ex + 7y, x = s/t, y = t/s dz %3D ds az at %3D

A: given z=ex+7yx=sty=ts

Q: Use the Chain Rule to find ôz/ðs and ôz/ôt. z = tan(u/v), u = 9s + 8t, v = 8s – 9t as az at

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Q: Find a relating ab and c Sothat the linear Systen X +2y- 2X +3 y +3Z = 6 5X +9y - 6Z = c eojarrar A…

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Q: du If u = x²y + y²z + z?x then at (1,1,0) is ax %3D -

A: Given that u=x2y+y2z+z2xTo find :∂u∂x  at 1,1,0Solution :u=x2y+y2z+z2x∂u∂x=2xy+0+z2∂u∂x=2xy+z2

Q: Let w = r = Uv, s = u - 3v. Use appropriate forms of the + s²' dw dw chain rule to find and in terms…

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Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv ,   y=3uv-uvw and…

Q: 비 az and Given that z = e*, x= 2u+ v, y= .y==. Find using the chain rule. au

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Q: Let f(r, y, 2) = 2ry + 2. Evaluate f(1, y, 2) dz where C is the portion of the helix r(t) = cos ti+…

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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 dz/ðs and öz/ðt. z = arcsin(x – y), x = s² + t², y = 1 – 8st dz 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: Use the Chain Rule to find az/əs and ôz/Ət. z = tan(u/v), u = 8s + 3t, V = 3s – 8t

A: z=tanuv,   u=8s+3t,   v=3s−8tFormula→∂z∂t=∂z∂u⋅∂u∂t+∂z∂v⋅∂v∂t

Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: (b) Find fx, fy and f,if f(x,y,z) = zln(x²ycosz). (c) Use chain rule to find du and 2 if z =;x =…

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

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Q: f (lnx + y) dx − a² dy, where & is the rectangle with vertices (1, 1), 1. Use Green's Theorem to…

A: Let I =∮(ln x+y)dx-x2 dy, where the region is C which is a rectangle with vertices…

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

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Q: Use the chain rule to find az az and as at z = (x - y)", x = s?t, y = st? az as az at

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Q: Write the chain rule for- at aw given that w = f(x,y,z); x = g(t), y = h(r,t), z = k(s,t)

A: We are given that w = f(x, y, z), x = g(t), y = h(r, t), and z = k(s, t). We need to write the chain…

Q: Use the Chain Rule to find ðz/ðs and az/ðt. Z = tan(u/v), u = 8s + 9t, V = 9s – 8t %3D az ds az at

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Q: Use the Chain Rule to find ôz/əs and əz/ðt. z = tan(u/v), u = 4s + 7t, v = 7s – 4t Əz as az II

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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: Prove that (x+) ) is the rolution on the dipporen tial equation y'+ y-e 9= C,e*+ C2x + Cg, y" - 4 y"…

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Q: Use the Chain Rule to find dw/dt. w = xey/z,    x = t7,    y = 1 − t,    z = 3 + 7t

A: We use the product rule then chain and quotient rule

Q: Use the Chain Rule to find az/as and əz/ət. Z = tan(u/v), u = 7s + 5t, V = 5s – 7t az ds az at

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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: az and ди az Given that z = exy, x = 2u + v, y = , find (using chain dv rule).

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Q: az Use the Chain Rule to find at for z = In(x? + y), x = st, y = t/s.

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Let z = √7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2.

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Q: Find Sc F dr for F = 2yi + 5x j+ 3zk if C is the helix æ = cos t, y = sin t, z = t, for 0 <t< 4T.…

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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 and compute if z = x2 + xy, x = uv? + w°y = u + ve"

A: z=x2+xy3, x=uv2+w3, y=u+vew

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: c) Use the Chain Rule to compute %3D ds se In (c) express your answer in terms of the independent…

A: Here, the given functions are: f(x,y,z)=x4y+z4, x=st2, y=st,z=s2t

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

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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: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

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Q: Use the Chain Rule to find əz/əs and Əz/ət. z = e' cos(0), r = st, V s8 + t8

A: Consider a multivariable function where and . Then the chain rule states that and .