SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE AI | DON'T USE AI IDON'T USE AI IDON'T USE AI I Answer the following question. Is it valid to apply the gradient and obtain a result of the following functions b) f(x, y, z) = (10xyz)i (10 cos(x)y²z)j - (27 si n(z)xy)k Justify your results. If yes, determine Vf, if not, explain why

Q: Find the directional derivative of the function at P in the direction of v f(x,y,z xy + yz + xz,…

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: x² 5x w Given that f(x) 3 a) find f'(x) b) find the equation of the tangent line x = 1. 1 12. Given…

A: Let's find.

Q: CLO 5 Find the gradient of the scalar function V=p2 cos?o at P(2,3.62,3). O a. 1.63 ap -3.15 ad O b.…

A: Given the scalar function V=ρ2cos2ϕ at P2,3.62,3

Q: (6) calculate the inrtantanco us rate of at point (4,1,2) in the change of 9 direction of the vector…

A: This is a question of multivariable calculus, the calculus of several variables.

Q: For Parts (a) (b), find the gradient at the given point. (a) f(p, q) — 6р? + 3q? + 2рq at (1, —2)…

A: Answer is mentioned below

Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: Use the Chain Rule to find at aw w = x² + y² + z²; x = 10tsin s, y = 10tcos s, z = 9st² əs Find the…

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Q: ) Using a drawing technique and a calculus method calculate the gradient when x=3 deitax 6 -10 311…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Suppose the temperature of a metal plate is given by f (x, y) = the temperature of the metal plate…

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Q: 3:) Consider the function g defined by g(x ,y) = cos( mxVy) + log3 (x-y) (b) calculate the…

A: Given,g(x, y)=cosπxy+1log3(x-y)To find: Instantaneous rate of change of g(x, y) at point (4,1,2) in…

Q: O Question 14 Y Suppose that f(x, y) =zy. The directional derivative of f(x, y) in the direction…

A: (.). Given ,         direction is   and at the point  .(.) Directional derivative of a function  in…

Q: 1. Consider the function g(x, y) = cos(xy) + sin(x – 2y) (a) Determine (c) Determine (c) What is the…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: 6. Express the following functions in the form u(r, y) + iv(r,y). (a) f(z) = +(1– 2i)z. %3D (b) f(2)…

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Q: 8. Let f(x, y)=x√√√x - y². (a) Find and sketch the domain of f. (b) Find the directional derivative…

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Q: Problems 1-4: Compute the gradient of the function at the given point. 1) f(x, y) - 4x2-2y. (-3,-4)…

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Q: Solve for the gradient of the given function. f(x, y) = e" sin y + e cos x

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Q: 3x 5y-2z 3) f(x, y, z)= tan-1. (-10, 0, 0) 4) f(x, y, z) - In(x2 + 4y2 + 3z2), (4,4,4)

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Q: 4. Now let's refresh Calculus I and find first derivative of (assume that variables are denoted by:…

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: Determine the directional derivative for f(x,y, z) = sin(yz) + In (x) at (1,1, 7) in the direction…

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Q: Find the gradient of the function f and evaluate it at the given point Po, f(x, y, z)=e+y cos z + (y…

A: As per our guideline, we are supposed to solve only first subpart. Kindly repost other subpart as…

Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: 1. Consider the function g(x, y) = cos(xy) + sin(x – 2y) (a) Determine g (c) Determine (c) What is…

A: Given function is  g(x,y)=cos(xy)+sin(x-2y) we have to find the second order partial derivatives…

Q: Find the gradient of f(x, y, z) = e³x+6y+6z grad f = + + T.6 T k

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Q: (i) If y =g (x1- x2). Let u = x1- x2, show that (a) ay/du = ây/Əxı=- dy/ax2 %3D (b) a@y/ðu² = y/Əx¡²…

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Q: Problem 1 Consider the function: S(z, v) = sin(2z + 3y). (a) Find the gradient of f. 2. (b) Evaluate…

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Q: Find the direction 0 in which the directional derivative of the function f(x, y) = æy+ y² at the…

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