5. If the gradient of f(r, y) at (1,2) is 2i – 2j, then the maximum and minimum values for a directional derivative of f at (1, 2) are respectively A. 2/2 and -2 B. -2/2 and v2 C. 2/2 and 2/2 D. 2/2 and -2/2

Q: If f(x,y,z)=xe^{4y}\sin(6z), then the gradient is

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Q: 1-Find the gradient of (1) f (x,y)= In(x²+y²) (1,1)

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Q: 7. Compute the gradient of the following function f(x, y, z)= e-2z sin(2y) cos(2y);

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Q: Find the gradient of the function at the given point.

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Q: Q2: a) If W =F(x,y), where x =v -g and y = 2vg calculate W +W, b) What is the directional derivative…

A: Given that w = Fx,y  , where x = v2 = g2 and y = 2vgWe have to calculate wx2 + wy2Now, we know that…

Q: ,2 For function f (x, y) x2+1 Evaluate the gradient at the point (1,2)

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Q: _12. What is the maximum directional derivative Daf of the function f(x,y,z) = x – y² + z² at the…

A: Let's find.

Q: f(x,y)=x² +16xy + y² +8

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Q: Find the gradient of the function at the given point f(x, y) = 5x + 4y² + 1, (1,4) Vf(1, 4) =

A: Solution of given question is written in below steps.

Q: If f(x, y, z) 2x5 + 3y5 — 8x2у?z?, - what is the partial derivative of f with respect to z? .A f z =…

A: Partial differentiation of  F(x,y,z) = 2x⁵ +3y⁵ - 8x²y²z² with respect to z

Q: Find the partial derivative of f (x, y) = e2+3y cos (x³y²) with respect to x. O fa (x, y) = e2x+3y…

A: Given f(x,y)=e2x+3ycosx3y2 To differentiate f(x,y) partially with respect to x Let u=e2x+3y…

Q: Q2: Discuss the fundamental theorem for gradients usingE = 5x2 î + 20 xy j+ 10 yz3 k and the…

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Q: Find the partial derivative of z with respect to u, if z = x^4+x(^2)y, x = s+2t-u and y=stu^2, when…

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Q: 2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

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Q: 1. Determine if the gradient of the following velocity function is irrotational: V (x, y, z) = 3x³y²…

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Q: 5) Find the gradient of o = x?yz + 4xz2 at (1, -2, -1).

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Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

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Q: Calculate the gradient of the tangent to the following curves at the given 1 y = 3x', x = 1 y = 2x –…

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Q: f(x, Y, z) =

A: We are asked to find the gradient of the function.

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 8,    (2, 1) ∇f(2, 1) =

A: We have to find the gradient of the function  f(x, y) = 2x+4y2+8  at the point (2, 1).

Q: 2. Let f(r, y) be a differentiable real valued function in two variables. If Vf (z0 m) = (f (ro,…

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Q: 1. Find the Gradient of the following F = x*e" - y': b. F, = 4x - 3y + 5=? а.

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Q: The gradient of f(x, y) = e'·² sin(2 - y) at (x, y) = (2, 1) is defined as followed: V f(x, y) =…

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Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

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Q: The function f whose gradient vector is vf(x,y) = (xIn(v + 7), 7x + y + 7> has two critical points…

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Q: Compute the gradient of each of the following functions. а. f(х, у, 2) %3D х sin(yz) b. f(x, y, z) =…

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Q: 4) Let f(x, y) = x² – 2xy a) Find the gradient of f at the point (1, –2). b) Use the result of (a)…

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Q: 1. Find the Gradient of the following a. F, = x'e" - y': b. F, = 4x' - 3y +5=?

A: Solution is given as below:

Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

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Q: Suppose that the real variables p, v, t, and u satisfy the equations f(p, v, t, u) = 0, g(p, v, t,…

A: Given that the real variables p, v, t and u satisfy the equations fp,v,t,u=0,    gp,v,t,u=0 We need…

Q: 1. Let f(x, y) = x cos(2x+ y). a) Find the value of the directional derivative of f(x, y) at in the…

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Q: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: (c). If y = f(x1, x2, u, v), where x =h(u, v) фу and- pu Find total derivative Also draw their…

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Q: 4. Find the gradient of the function f(x, y) = cos(x² + y²) at the point (3,-4). 5. Find the…

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Q: -1/2 Find the gradient of f(xy.z) = (x² +y² +z?) + In (xyz) at the point (2, – 1, - 2).

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Q: Find the gradient of the function at the given point. In(x² – y) – 3, (3, 8) z = 1 Vz(3, 8) = 2i

A: I have checked the work. Calculation is correct.

Q: 1. Find the directional derivative of g(r, y, 2) = :2 - zy + 2y? at P = (2,1, -3) in the direction…

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Q: 2. Find the maximum value of the directional derivative, D f, of the function _2 f(x, y, z) = x´ +…

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Q: Find the partial derivative of z with respect to x дz (2x−y) дх Н дz 2 О 0 = 3 - 1 " дх Т 2y 2y дz…

A: Just use the rule of partial derivative and find the required solution.Final solution is in the box.

Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

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Q: 12 Use the gradient to find the directional derivative of the function at Pin the direction of Q.…

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Q: 1. Find the directional derivative of the function f (x, y, z) = In (3x + 6y + 9z) at the point…

A: To find: the directional derivative of the function f(x,y,z)=ln (3x+6y+9z) at P1(1,2,3) in the…

Q: If ø = 3r²y – y³,2. Find gradient Vø at the point (1, –2, –1).

A: The solution is given as

Q: If f(x,y,z)=xe^(2y)sin(8z), then the gradient is ∇f(x,y,z)=

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4) Vf(1, 4) =

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Q: 4. If f(x, y, z) = x sin yz, (a) find the gradient of f and (b) find the directional derivative of f…

A: