1) Find the directional derivative of f at the given point P in the direction of the point. Q- f(r, y) = 4ry 2a2, P (3,6), Q= (1,9)

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: 2. Find the directional derivative of o = yx2 +x²z + 3xyz in the direction of vector n = î + 2 ŷ -2·

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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: Find the direction derivative of f(x, y, z) = x²y -zx -yx at the point (1,-1,1) in the direction…

A: Directional derivative using gradient

Q: Find the directional derivative off at the given point in the direction indicated by the angle 0.…

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Q: p) What is the directional derivative of /(x,y,z)=(x+2y+3z)* at point (1,-1,1) in the direction of…

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Q: O Find the directional derivative of f(x, y) = 3x² – 3y² in the direction from P(-,0) to Q(0, 1).

A: Point is given so first find the direction unit vector then  dot product with divergent of f(x,y)…

Q: 3. Prove that the directional derivative of f(x, y) = y² + 2xy³ + x²y² at point (0, 1) in the…

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Q: Find the directions in which the directional derivative of f (x, y) = ye*y at the point (0,2) has…

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Q: 6.) Find the directional derivative of g(x,y)=Vx² +y² at the point P(3,4) in the direction of v…

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Q: Find the diectional derivative of the function f (xiy,z)= sin (xy+2) at the point of P(1, al2 x4) a…

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Q: Calculate the directional derivative direction Q(5,4) 4 3√-3x²-5xy3 of at P (1,-2) in the

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Q: Suppose that f (1,2) = 3 and that the directional derivative of f at point (1,2) in the direction of…

A: Given : f1,2=3 and the directional derivative of f at 1,2 in the direction of the vector i+j is…

Q: Find the directions in which the directional derivative of f(x,y) = x^2 + xy^3 at the point (2,1)…

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Q: Find the directional derivative of f(x, y) = x2y3 + xy2 in the direction ~v =< −3, 7 > at the…

A: f(x, y) = x2y3 + xy2 Please see the white board for the partial derivatives at the point (-1,…

Q: 2y Find the directional derivative of f(x, y, z) = x + z at P(4,4, –3) in the direction from P to…

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Q: The directional derivative of f(x, y) = In(x² + y²) at the point P(-5, 21) in the direction i = (9,…

A: Given  fx,y=lnx2+y2 To do find the directional derivative of fx,y at the point P-5,21 in the…

Q: Suppose we know that for a function f we have Vf(x, y) = (6x, 6). Find the directional derivative of…

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Q: 8y If the directional derivative of f(x,y)%D at (2,1) in the direction of (2a,-3) is equal to zero,…

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Q: Find the directional derivative of f at the given point in the direction indicated f(x,y) = cos(xy),…

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Q: Find the derivative of the function f (x, y, z) = -9x + 5y – 10z at the point (-3, 6, 5) in the…

A: we have to find the following . I have explained in details please see the explanation and if any…

Q: (a) Find the directional derivative of f(z, y) = ry + y at the point (1,2) in the direction (1,1)

A: Solution a: Given function is f(x, y)=xy+y Now gradient of the function is ∆f(x, y)=∂f∂x, ∂f∂y⇒∆f(x,…

Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: Find the directional derivative of f at the given point in the direction indicated by the angle θ.…

A: Given, 4. f(x,y) =xy3 - x2, (1,2) , θ = π/3

Q: Q2 / Find the directional derivative of f(x.y.z) 4xy +5xz2 +6yz2 At the point P(3,1,4) in the…

A: ∂f∂x=4y+5z2∂f∂x=84∂f∂y=4x+6z2∂f∂y=108∂f∂z=10xz+12yz∂f∂z=168Therefore, the gradient is∇f (3, 1, 4)…

Q: b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction…

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Q: Find the directional derivative of Ax,y,2) = xy+ 4y²z+3xz? at the point (3,-1,2) in the direction of…

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Q: Suppose that f(r, y) the point (r, y) 3 (6, ry. The directional.derivative of f(z, y) in the…

A: Given:  fx, y=xy To Find:  To find the direction derivative of fx, y at the point x, y=6, -4, in the…

Q: Suppose that f(x, y) = xy. The directional derivative of f(x, y) in the directional and at the…

A: Explanation of the solution is given below....

Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: Find the directional derivative of f(x, y) = Vxy at P(9, 1) in the direction from P to Q(12, -3).…

A: Given that: f(x,y)=xy        at P(9,1) in the direction of Q(12,-3)

Q: Which of the following values is the directional derivative of f (x, y) = 3x² + xy – 2y² – yz + z?…

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Q: Find the directional derivative of the function at point P in the direction of v. 3 u = 4 f(x, y) =…

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Q: Find the directional derivative of F(x , y , z)=7y2e−x+3z2 in the direction u=(3,6,−2) at the point…

A: We have to solve

Q: Find the directional derivative of f(x, y) = Vxy at P(3, 3) in the direction from P to Q(6, -1).…

A: Using partial derivatives at (3,3) in direction of PQ.

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

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Q: Prove that the directional derivative of f(x, y) = y + 2xy³+x²y2 at point (0, 1) in the direction…

A: The gradient is just the vector of partial derivatives. The partial derivatives of f at the point…

Q: Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1,…

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Q: 10. Let f(x, y) = x² + y³. Calculate the directional derivative of f in the direction of = (4, 3) at…

A: The given function is: f(x,y)=x2+y3Direction vector is:  v→=4, 3Given point:  P=(1, 2)

Q: Let v = (3,4, 12) . Find the directional derivative of f(x,y, z) = x – y² +3z³ in the direction of…

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Q: If f(x, y, 2) = cos(x - y)+e² , compute directional derivative of f at (5, 5, 0) in the direction of…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of  PQ.…

A: Given problem:- Find the directional derivative of the function at P in the direction of PQ. f(x, y)…

Q: Ctiofnal g(x, y) = V x² + y², _P(5, 12), v = 3i – 4j -

A: The partial derivatives of f at point (x,y)=(5,12) are :…

Q: If u = and Vf (-2, 5) = 3u, then the minimum value of the directional derivative Dy f (-2, 5) is…

A: We will use concept of minimum value of Directional Derivative and its direction

Q: Find the directional derivative of w=2x²yz in the direction of v=3i-4j at the point (-1, 1.13)

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Q: Explain why, when u = ⟨1, 0⟩ in the definition of the directional derivative, the result is ƒ(1a,…

A: Formula:  Du f(a) =limh→0 f(a+hu)-f(a)hu=1, 0…

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

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Q: Find the directional derivative of the function f(x, y) = In(x² + y*) at the point (– 3, – 1) in the…

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