Find the directional derivative of o(r, y, z) = r-zry? - z at the point Po = (1, 1,0) in the direction of i = 2i – 33 + 6k. In what directions does 6(1, y, z) change most rapidly at Po, and what are the rates of change in these directions?

Q: Find the directional derivative of z = f (x, y) = x²y³ – 3y² at (-3,4) in the direction of the…

A: Use directional derivative formula which is mentioned in solution.

Q: Find the derivative of the function f(x,y,z) = x² + 2y² – 3z² Po = (1,1,1) in the direction of at…

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Q: find the directional derivative of the function at P in the direction of PQ.

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Q: Find the directional derivative of the function at the given point in the direction of the ved f(x,…

A: The formula for the directional derivative is given by , where is gradient of the function, f(x,y)…

Q: (a) Find the derivative of f(x, y, z) =x²- xy²- z at Po(5, 1, 0) in the direction of v=2i-3j+ 24k.…

A: Given: f(x, y, z) = x2 - xy2 - z, P0(5, 1, 0) and v=2i - 3j + 24k.

Q: Find the derivative of the function at Po in the direction of A. h(x, y, z) = cos xy + e + In zx,…

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Q: Find the directional derivative of f(z, y) = In(e"- 3y) at the point (0, 0) %3D in the direction of…

A: Topic- Direction derivatives of function using partial differentiation .

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: 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: 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: Find the directional derivative of f(x, y) = cos(x) + y² at (T,2) in the direction of (3, –4).

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Q: (d) Find the directional derivative of f(x, y) = x²e¬y at (-2,0) in the direction towards the point…

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Q: b) Find the directional derivative of f (x, y) = xy + e*°vy + 1 at (-1,1) in the direction of the…

A: f=xy+ex3y+1 take the partial derivative with respect to x   fx=∂∂ xxy+ex3y+1 fx=∂ ∂ xxy+∂ ∂ xex3y+∂…

Q: Find the derivative of the function f(z, u) = =*y – 4y° at the point Po(2, 1) in the direction of =…

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Q: The directional derivative of f(x, y) = 2e* cos y at (0, ) in the direction of v = (-6, 8) is

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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: b) Find the directional derivative (D.) of the function at P in the direction of PQ f(z, y) = sin 2z…

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Q: Find the derivative of f at point P in the direction of u. f(x, y, z) = 6x² + 2y – 7z?, P = (8,–6,…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the derivative of the function at Po in the direction of u. X- y g(x,y) = Po(- 1,1), u= 12i +…

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Q: Find in what directions does flx, y, z) = 4x 2– 9z + 2z In(y) increase and decrease most rapidly at…

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Q: The directional derivative of f(, y) = In(x² + y²) at the point P(1,5) in the direction v (3, 4) is…

A: We have to find the directional derivative of the function fx, y=lnx2+y2 at the point 1, 5 in the…

Q: Find the directional derivative of f at the point p in the direction of a. F(x,y)=y² ln x; p=(1,4)…

A: The given function is Fx,y=y2 lnx with p=1,4  and  a=i-j. Computation 1: Obtain gradient of f  as…

Q: Find the directional derivative of f(x, y, 2) = xz+ y?, at (1, 2, 3) in the direction of i = i+j+ k.…

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Q: The directional derivative of f(x, V, 2)=y-vz at the point (2, 1,1), in the direction of the tangent…

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Q: The directional derivative of f(x, y) = -e" cos y at (0, ) in the direction of v = (-6, 8) is 14 O…

A: Here,

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: Compute the directional derivative of the function f(x, y, z) = 3xyz at the point P = (1, −3, −1) in…

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Q: Find the directional derivative of h(x,y) = e*(sin y) at the point (1, T/2) in the direction of v =…

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Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1, 1) in the direction of from…

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Q: 3. Find the derivative of the function f(r, y, ) = xy + yz+ the direction A = 3i + 6j – 2k. zr at…

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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: The directional derivative of f(x, y) = -e" cos y at (0, ) in the direction of v = (-6,8) is

A:

Q: The directional derivative of 2e" cos y at f(x, y) = -2e* cos y at (0, 7) in the direction of v =…

A:

Q: Find the directional derivative of f (x, y) = e" /Ty at the point (1,16) in the direction of the…

A: From the given problem:   fx,y=exxy ; p1,16   And the direction of the negative y- axis means :…

Q: Find the directional derivative of f(x, y) = In(e- 2y) at the point (0, 0) in the direction of 3i +…

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Q: Find the derivative of the function at P.(0,0,0) in the direction of B. f(x, y, z) = 3e* cos yz,…

A: Directional derivative of the function.

Q: Find the directional derivative of f(x, y, z) = x²y²z + 4xz at (-1,2,1) in the direction 2i + j +…

A: We have to find the directional derivative of f(x, y, z)=x2y2z+4xz at (-1, 2, 1) in the direction…

Q: The directional derivative of f(x, y) = e" cos Y at (0, ) in the direction of v = (-6, 8) is

A:

Q: Find the directional derivative of f(x, y) = In(e" - 2y) at the point (0,0) %3D in the direction of…

A: take the partial derivative with respect to x put the point (0,0)

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: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 3 ex cos (yz),…

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Q: Find the derivative of f at point P in the direction of u. f(x, Y, 2) = 9a² + 2y² – 72², P = (6,7,…

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Q: Find the directional derivative of * f (x, y) = 2e* cos y at (0, 7) in the direction of v = (-6, 8)…

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Q: 1. Find the directional derivative of f(x,y) = y²e²" at (0, 1) in the direction of v =.

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Q: Find the directional derivative of f(x,y,z) = x³ + 3xy + 2y + z? at (1,1, 1) in the direction of v =…

A: We will use the fact that the directional derivative of a function at a point in the direction of a…

Q: The directional derivative of f(x, y) = e" cos y at (0, ) in the direction of v = (-6,8) is

A:

Q: Find the values of constants a,b.c such that the maximum value of the directional derivative of f…

A:

Q: 1. Find the directional derivative of the function f(x, y, z) = 3e" sin(ry) in the direction of v =…

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Q: Find the derivative of f(x,y) = xe² +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j .

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The directional derivative of f(r, y) =-e" cos y at (0, 5) in the direction of v = (-6, 8) is

A: Given that fx,y=-excos y at0,π4and v=-6,8