QUESTION 5 Let f (x, y) = x sin y be given. For which choice of x and y, where x = g(s, t) and y = h (s, t), partial derivatives of f with respect to s and t will satisfy af = 3 as af Əx and af at af ду a. x = stt, y = 5- 2t O b.x = 3s+ 5t, y = 25 + 3t Ocx = 35 + t, y = 5s +t O d.x = 35, y = 5t O e.x= 35?, y = ?

Q: Find the direction derivative of f(x.y.z)-xy'z at the point p(3,2,1)in the direction towards…

A: To find the directional derivatives

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Q: Determine the second-order partial derivative for the indicated function f(c,y) = cos(2x² – 3y?)…

A: Partial derivative of a function g(x,y) with respect to x is the derivative of g(x,y) keeping y…

Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

A:

Q: The temperature at the point (x, y) on a metal plate is X x² + y² Find the direction of greatest…

A: Given function:-T=xx2+y2

Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

A:

Q: xy Find all second order derivatives for r(x,y)= 4x +9y

A: The given function is

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Q: a) Suppose you are given model with two explanatory variables such that: Y₁ = a + B₁x₁i + B₂x₂₁x +…

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Q: Find the directional derivative of f(x, y, z)= = in the direction from P to Q(2, 4, -1). NOTE: Enter…

A:

Q: Find the gradient Vf and the directional derivative at the point P (1,–1,2) in the direction a =…

A: The given function f(x, y, z) = x3z - yx2 + z2.The gradient of a function f is defined as∇f(x, y, z)…

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A: Given function is  V=x^2 sin(y)cos(z)

Q: If f(x, y, z) = 4zy², then the gradient at the point (5, 2,5) is Vf(5, 2, 5) =

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Q: a) Describe the curve obtained when we make y = 2 and 2= √2 a f b) Represent on this curve the…

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Q: 3+ 2x² + y², find all second derivatives 5. For the function f(x, y) = v fe: fy and f"y. Show that…

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Q: b. Find the angles 0 (with respect to the positive x-axis) associated with the directions of maximum…

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Q: f(x) = x³ - 5ex + 7x Find the first 2 values of the derivative vector when the derivative of the…

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A: Function, Tx, y, z=x2y+y2z

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A:

Q: Solve the partial differentiabion equation +6.0 = 2-y Ox Show that the gereral aoludion 2.

A: Given. the partial differential equation                            ∂2z∂x2+5∂2z∂x∂y+6∂2z∂y2=2x-y…

Q: e) s = cos (1– 21) -2 4t f) y = t+1, .2 x + x g) y =

A:

Q: Suppose the equation z²+z+x+y³: = 4 implicitly defines z as a function of x and y. At the point (x,…

A: