Consider the functions f(x, y, z, t) = (x² + 2. t²) and g(u. v) = (uy, u +v. u – v). Use the chain r

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: Is the map T: R² → R² given by T(x, y) = (x,y + 1) linear?

A: T: V-> W  mapping from V to W is a linear map if and only if  ->(u+v)=T(u)+T(v) ->T(au) =…

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: Integrate ƒ(x, y, z) = (x + y + z)/ (x2 + y2 + z2 ) over the path r(t) = t i + t j + t k, 0 <…

A: The equation of the parametric curve (path) is:   Path r(t) = x(t) i + y(t) j + z(t) k   And the…

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 dw/dt. w = xey/z,    x = t5,    y = 1 − t,    z = 3 + 7t

A: To find out dw/dt.

Q: Demonstrate that the functions Y1 = a", y2 = sin(x), Y3 = xe* are linearly independent on R. 9.

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Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x2 + y2 x = 5t, y = 3t t = 2 dw dt…

A: Please refer the attached image for complete solution.

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: The divergence of the vector F = a²yî + æyz} – a*y°k is x2 y? k is -

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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: For x = x(y + 3), y = y(x - 1), find the trace of the Jacobian at the fixed point x = 0, y* = 0.

A: Given system is x˙ =xy+3y˙ =yx-1 Fixed point :  x* =0, y*=0   Take   x˙ =fx, y,    y˙ =gx, y   then…

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = (x + y + 2)2 at a. (0, 0), b.…

A: Given function,  f(x, y) = (x + y + 2) 2 To find linearisation L(x, y) at i) (0, 0)  ii) (1, 2)

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: Use the Chain Rule to calculate dt f(x, y) = 5x – 2xy, r(t) = (t2, t - 4t), t = 4

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Q: Solve the following function by applying the chain rule. w = xyz x = u?v y = uv? Z = u? + v? %3D…

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Q: Use the Chain Rule to find dw/dt. w = xey/z,    x = t5,    y = 3 − t,    z = 1 + 2t

A: Please find the detailed solution in below image

Q: Let f(x, y) = x?y? and e(t) = (t, t³) (a) Calculate: Vf•d (t) = d (b) Use the Chain Rule for Paths…

A: Solve by chain rule

Q: Use the Chain Rule to calculate f(c(t)). dt f(x, y, z) = xºy®e4z, c(t) = (t², t³, t – 1), t = 1…

A: To Determine: Use the chain rule to calculate:                                       When…

Q: Using the chain rule, find df/dt in terms of t if, f(x,y)=xsin(y) and x = 5*t,  y = t^2

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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 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 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: Use the Chain Rule to find- af when r = 2, t =-1 of the function ar f(x, y, z) = e3xyz cos 2xyz ; x…

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Q: Let f(x, y) = 8x + 2y2, r(t) = (cos(t), sin(t)). Use the Chain Rule to calculate f(r(t)). !! dt…

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Q: xy ) Suppose thot fixy)=e , x(4,0)= 3uSiina, glu, vl = f(x (4,v), yluiv), find , by using Chain Rule

A: Using the chain rule,

Q: Let f(x,y)=xy^2 and r(t)=⟨(1/2)t^2,t^3⟩. Use the Chain Rule for Paths to evaluate d/dtf(r(t)) at…

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Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x2 + y2 x = 2t, y = 5t t = 2 dw dt…

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Q: Find dw/dt using the appropriate Chain Rule. Function Value w = x2 + y2 x = 3t, y = 5t t = 2 dw dt…

A: If W is a function of x and y. Also both x and y are function of t then the derivative of W wrt t is…

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: (a)

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: To find the linearization Lx,y,z of the function at the given points fx,y,z=x2+y2+z2 at 1,0,0

Q: Integrate f(x,y,z) = (x + y +z)/ (x² +y² +z? over the path r(t) =t i+tj+3t k, 0<a<t<b.

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Q: Use the Chain Rule to calculate dt (r(e)). f(x, y) = 3x – 2y, r(t) = (t°, t°), t = 2 (2, 8), t = 2

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Q: se the chain rule to compute and at (u, v) = (1, I) where f(x, y, z) = x²y + y²z + z²x and r(u, v) =…

A: Given: fx,y,z=x2y+y2z+z2xr→u,v=eucosv,eusinv,u2u,v=1,π4 To find: ∂f∘r→∂u=?∂f∘r→∂v=? Concept used:…

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 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: Let z = f(x, y) = e**y while x = 2st and y = s² + t³. Use a chain rule to find ôz/8t at the points…

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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: For a scalar function f(x, y, z) = x? + 3y2 + 2z?, the gradient at the point P(1, 2, - 1) is

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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/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: Find the linearization of the function f(x, y, z) = xy+ yz + zx at the point (1,1,1).

A: Linearization of the function f(x,y,z) at (a, b, c) is given by…

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 .