Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

Q: If y = Vx(3 – x)², show that- dy (3-х) (3-4x) Find the x coordinates of %3D dx all points on y =…

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Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

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Q: Find the directional derivative of f(x, y) = (xy)^1/2  at P(6, 6) in the direction from P to Q(9, 2)

A: The directional derivative (D.D) of function f at point P in the direction of vector a is given by,

Q: integrate ​f(x,y)=x2−y over the curve​ C: x2+y2=4 in the first quadrant from (0,2) to 2,2.

A: The solution are next step

Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

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Q: y''(t)+5y'(t)+4y(t)=u(t) u(t)=2e-2t , y(0)=0 ,y'(0)=0 Y(s)=?

A: The solution is given as

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 a gradient of the equation: F(x,y) = v2x + :- y sin a + 4 VF =?

A: Here, the given vector equation is: F(x,y)=2x+xy-y2sin x+4

Q: The equation of line normal to f(x) = (x +4)^(1/2) at Q (0,3) is

A:

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 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: dy If y (t+ 2t + 6) (7t + 6), r find dt dy dt

A: Given  y=t2+2t+67t2+6y=7t4+6t2+14t3+12t+42t2+36y=7t4+14t3+48t2+12t+36

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: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-2, 0, 0)…

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Q: Find the directional derivative of f(x, y, z) = x²y + y²z v = at P(1,2,3) in the direction of %3|

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

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: dy If y = (t + 2t + 5) (7Ł² + 3), find dt dy dt

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Q: Find the direction at which the function f(x, y, z) increases fastest at (2, 0, 0) = x In(e' – xz)…

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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: |dx + N(x,y)dy = 0 x² + y,

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Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

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: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

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: 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: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: dy - f *P, = 7 dt y(0) = 4.

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Q: Q1: Find the derivative of f(x,y,z)=x^3-xy^2-2z at point P_o (1,1,0) in the direction of vector…

A: Solution:-

Q: Find the direction at which the function f(x, y, z) = x In(e – xz) increases fastest at (-2, 0, 0)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The directional derivatives of fx, y,z) = xy+ 4y°z+ 3xz? at (3,3,3) in the direction of y = 31 + 6j…

A: The function is f(x,y,z)=x3y+4y2z+3xz2 at the point 3,3,3 in the direction of v→=3i→+6j→+6k→. Find…

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) = x²e²y in the direction of i = (1, –1).

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

A: Given,            f(x,y)=8yx

Q: ) Compute the directional derivative of f(x, y) = x2 y at the point (1, 1) in a direction normal to…

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Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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Q: dy dæ at x = 2 if y = 3x + 5 and dt Find - 2. %3D %3D - dt dy %3D dt

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Q: Find the differential of f(x, y) = vx2 + y³ at the point (1,2). df

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Q: 23. Find the directional derivative of f(x, y) = *+y at P(1,0) in the direction of Q(-1,-1).

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Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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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: Use the definition of directional derivative to solve Duf(xo, yo, zo) at point P(xo, yozo) where…

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

Q: Compute ∫C y dx + xy dy if C goes from (0, 0) to (1, 2) along the line parameterized as x = t, y =…

A: Here I am attaching image so that you understand each and every step.

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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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: Find the direction in which the function f (x, y, z) = xy - In z is increasing most rapidly at the…

A: We will use directional derivative here

Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-3,0, (0,…

A: Sorry I cannot recognize your given points. So I provide only methods of problem you can easily…