dz dz and ds' dt C) Use the chain rule to compute for dsðt

Q: use the chain rule to find dz/dt or dw/dt w=xey/z, x=t2, y=1-t, z=1+2t

A: Given

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

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Q: Use the Chain Rule to calculate f(r(t)). dt f(x, y) = x³ - 5xy, r(t) = (cos(4t), sin(5t)), t = 0…

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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: 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: ®. *,(t)=l, tilt)=t, Xglt) =t² Let [oD. Use Gran-Schridlt on er thogonolize e, 2) process to

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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: f(x, y, z) =(x²+y²+z) 2

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Q: Find a piecewise smooth parametrization of the path C. (ti + tj 0 sts 1 r(t) = 1st< 2 y = VI (1, 1)…

A: C:y=√x

Q: Evaluate eVf •dr where f(r,y, 2) = 4rye² and C is the path parameterized by r(t) = cos² t i +…

A: Given: fx,y,z=4xyezrt=cos2ti+sin2tj+tantk0≤t≤π4 Formulas used: ddxxn=nxn-1ddxex=exddxfgx=f'gx·g'x…

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: 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: Derive a Dirichlet principle for the elliptic operator L in divergence form with A e C² and b= 0.

A: Given elliptical operator L~ in divergence form with A∈C1 and b=0. Suppose A∈C1Ω of the second order…

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: Find a piecewise smooth parametrization of the path C. (ti + tj 0 ≤t≤ 1 r(t) = 1 y 1 ≤t≤2 [y=√x (1,…

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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: 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: 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: 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: f(x, y) =(e-2y)Cos2x

A: The Laplace equation is: ∂2f∂x2+∂2f∂y2=0

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: 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: Find the circulation of F = 2xi + 2zj + 2yk,r(t) = ti + (1-t)j,t %3D %3D E [0,1]

A: Here we have to find the circulation of      F=2xi+2zj+2yk, r(t)=ti+(1-t)j , t∈[0,1] .

Q: Consider the following. w = xyz, x = s + 4t, y = s – 4t, z = st? (a) Find aw/ds and ôw/at by using…

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Q: Find the Laplace of f(t) = (e-3t - e5t )2

A: To Find L(e-3t-e5t)2: Expand (e-3t - e5t )2: (e-3t-e5t)2=e-3t2-2(e-3t·e5t)+e5t2…

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: Evaluate I = Jc(sin ¤ + 2y) dx + (2x + y) dy for the nonclosed path ABCD in the figure. D А 3 (0,0),…

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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 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 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: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

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

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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: 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/ðs and dz/dt. z = tan(u/v), u = 3s + 6t, v = 6s – 3t dz %3D as Ot

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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 .