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

Q: Please show your answers to at least 4 decimal places. Suppose that f(x, y) = ry. The directional…

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Q: (a) Find the directional derivative of f (x,y) = In(xy) at (-) in the direction of (1,1).

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

Q: find the directional derivative of f(x,y,z)=3e^xcos(yz) at P(0,0,0) in the direction of A=2i+j-2k

A: First find out the partial differentiation of f(x,y,z) and then put the values (0,0,0) and then for…

Q: Find the directional derivative off 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) = 1+5x/ỹ at the point (5, 1) in the…

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Q: In what direction does g have the maximum directional derivative at (x, y) = (4, 1)? What is the %3D…

A: We have to find maximum directional derivative.

Q: Find the directional derivative of f(x, y) 6x at P(3,0) in the x + Y direction of Q(0,–2). NOTE:…

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Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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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(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 directional derivative of the function f(x, y, z) = ryz in the direction normal to the…

A: We havefx,y,z=xyz

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

A: We are asked to find directional derivatives of function.

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

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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: 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: Calculate the directional derivative of f(x,y)= In( Vx +y ) at point (1,1) in the %3D direction of v…

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Q: Find the directional derivative of f(x, y) at the point (9,0) in the direction indi- -8y xe cated by…

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

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Q: Find the directional derivative of the function f(x, y) = x² + y³ at the point (2, 1) in the…

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Q: Find the directional derivative of f(x, y) = 3x² - y² + 5xy at (2,-1) in the direction of -3i - 4j.

A: given function f(x,y)=3x2-y2+5xy given point (2, -1) given direction u→=-3i-4j We have to find the…

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: 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: 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 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 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: Find the directional derivative of f(x,y) = sin(x+2y) at the point (1, -3) in the direction θ=3π/4

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

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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

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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 f(x, y) = e*y + eY at the point (1,3) in the direction of the vector

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Q: , (a) Find the directional derivative of at (-2,1) in the direction u = ?-j. X.

A: Since you have asked a different question. I am answering the first one. Please post the question…

Q: f(x, y) = e2Y sin(x), P(0, 0), Q(2, 1)

A: Use the formula for the directional derivative and simplify.

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: Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0,–3,5)

A: Solution: The objective is to find the directional derivative of the given function

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

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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

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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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