Find the directional derivative of the function f(x, y, z) = 3e" sin(xy) in the direction of v = 3i – 4j +

Q: Find the directional derivative of the function xy2 + yz2 + zx² along the tangent to the curve x =…

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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 directional derivative of the function at P in the direction of v. h(x, y, z) = P(1, 4, 8),…

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Q: Find the directional derivative of the function at in the direction of A where g(x, y, z)=3excosyz…

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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: Find the directional derivative of f(x, y) = x² sin(2y) at (1, 7/2) in the direction of ở = 3i– 4j.

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Q: Find the directional derivative of f(x, y) = 3x2 − 2y2 at (−3/ 4, 0) in the direction from P(−3/4,…

A: The directional derivative is the scalar product of the derivative of the function to the vector…

Q: Find the directional derivative of f(x,y) = 2x –y´ at the point (1, 3) in the direction toward the…

A: We have given f(x, y) = 2√x – y2 and the point (1, 3).

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

A: The maximum value of a function f occurs in the direction of the gradient of the function f and this…

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: Find the directional derivative of the function at the point in the direction of the unit vector. 3…

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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: Find the directional derivative of f(x, y, z) = cz+y² at (1, 0, 4) in the direction of a =. = IZ

A: Differential equations are those equations of mathematics that involve dependent variables ,…

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

A: Given that: fx,y=2sinxy,               0  ,  5

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Formula to find the directional derivative in the direction of the given vector helps to find the…

Q: Find the directional derivative of f(x, y) = V5x + 3y at the point (0, 2) in the direction 0 3…

A: f(x,y) = 5k+3yt point (0,2)in direction θ= 5π4 radiusto find directional derivativesolution1)…

Q: Determine the directional derivative of f(x, y, z) = xe³+xsinz+x²y at the point (2,0,4) in the…

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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 the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

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: Use the gradient to find the directional derivative of the function at P in the direction of Q f(x,…

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Q: Find the directional derivative of the function at point P in the direction of v. h(x, y, z) = xyz,…

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Q: ) Find the directions in which the directional derivative of f (x,y) =4x2+sin (5 xy) at (1,0) has…

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

A: Given, f(x,y)=x2+4y2 at the point P=(3,2)

Q: Find the directional derivative of the function f(x, y) =1+5zj at the point (5, 1) in the direction…

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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: Find the direction in which the directional derivative of f(x, y) = x? + sin(xy) at the point (1,0)…

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Q: Find the directional derivative of f(x, y) = In(e* y) at the point (0,0) in the direction of 3i + 4j

A: We will use formula for finding directional derivative.…

Q: Find the directional derivative of f(x, y, z) = xz + y°, at (3, 2, 1) in the direction of 3 = 1+3+…

A: We need to find gradient of f at point (3,2,1)

Q: What is the directional derivative of the function f(x,y) = 2xy- 3y2 at point po= (5,5) in the…

A: Givenf(x,y)=2xy-3y2 ; p0=(5,5) ; u=4i+3jWe need to find directional derivative Duf(5,5)where…

Q: Find the directional derivative of the function at the point in the direction given. f (x, y, z) =…

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Q: Find the directional derivative of f(x, y, z) = xy + z 3 at the pointP = (3, -2, -1) in the…

A: fx, y, z=xy+z3,  P=3, -2, -1. Now, ∂f∂x=y·1+0=y∂f∂y=x·1+0=x∂f∂z=0+3z2=3z2 Now, ∇fx, y, z=∂f∂x, ∂f∂y,…

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: Let f(x, y) = sin(x – y). Calculate the directional derivative of f in the direction of v = (1, 1)…

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Q: Find the directional derivative of the function in the direction of u = cos(e)i + sin(@)j. F(x, y)…

A: Explained below

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

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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,…

A: Given that: f(x,y)=8sin(xy),    at (0,4)

Q: Find the directional derivative of f(x,y) v = 3i – 4j. x² sin 2y at (1, 7/2) in the direction of |

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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: 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: Find the directional derivative of the function f(x, y) = √√√x + 2y at the point (2, 1) in the…

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Q: Find the directional derivative of the function f(x, y) = In(x + y²) at the point (1, - 1) in the…

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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: Find the directional derivative of the function at P in the direction of v. f(x, y) = 8x-4xy+3y,…

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y*) at the point (2, 1) in the…

A: we will find the directional derivative

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

A: We have to find the directional derivative of f(x,y,z) at 0,1,12 in the directions parallel to the…

Q: Find the directional derivative of the function f(x, y) = In(x + y?) at the point (– 1, – 2) in the…

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Q: Find the directional derivative of the function at P in the direction of v. f (x, y) = 3x – 4cy+ 9y,…

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