Find the directional derivative of the function at the given point in the direction of the vector v. h(r, s, t) = In(3r + 6s + 9t), (1, 1, 1), v = 4i + 12j + 6k Dyh(1, 1, 1) = %3D

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

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Q: Let g(x, y) = e*^2 -vy (a) Find the directional derivative of g at (1, 1) in the direction of the…

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

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

A: the vector field is  g(x,y,z)=(x+4y+3z)32  point (2,1,1) to find the directional derivative in the…

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A: We know that; The expression for the gradient vector: ∇fx,y=i∂∂x+j∂∂yfx,y=i∂fx,y∂x+j∂fx,y∂y Given:…

Q: 1) For f(x,y, z) = x² – (1 – y)² + z². Find directional derivative of f at P(1,1,1) in the direction…

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Find the domain of the vector-valued function. r(t) = n(t) 0 (-∞, +∞0) O (1, + ∞ ) O (0, +∞ ) O [1,…

A: Find the domain for all three components and then take intersection of those.

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

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Q: Find the unit tangent vector for the vector function : r(t) = (t2 + 1,3 t, t3> %3D (1+4t2+9t)3…

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Q: 5. For a given function f(x, y) = Vx² +y² , what is the directional derivative of f at any point…

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Q: at the point (0,0) 1+y Which of the following is the directional derivative of f(2, y) in the…

A: The gradient is the partial derivative of a multivariable function. The gradient of a function tells…

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Q: Calculate the directional derivatives of the function x²y x²+ y? for (x, y) +0 f(x,y) = for (x, y)…

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Q: Find the directional derivative of the function f(x ,y ) = x^2 + xy at the point P.(1, 2) in the…

A: NOTE: Refresh your page if you can't see any equations. . the unit vector is the given point is

Q: Find the directional derivative Duf(P) of f(x, y, z) = x²y?z²at the point P(1, 2, 3) in the…

A: We have to find the directional derivative of f(x,y,z).

Q: -2 -1

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

A: Applications of derivatives

Q: Find the directional derivative D, f(2, –3, -3) for the function f(x, y, z) = ry + yz + zx in the…

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Q: Find the gradient vector, Vf, for the function, f(x). f(x, y) = x²y² + ex²y b. f(x,y,z) =x²y*…

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

A: In this first we calculate derivative of g function then get a unit vector in the direction of v. So…

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

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: b. Find the directional derivative of the function f(r, y, z) = re" + ye + ze" at the point (1, 1,…

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Q: Find the directional derivative of the function in the direction of the unit vector u = cos e i +…

A: This question is based on del operator.

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

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

A: The objective is to find the directional derivative of the given function h(r,s,t) along the point…

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Q: h (r, s, t) = ln (3r + 6s + 9t), (1, 1, 1), v = 4i+ 12j + 6k

A: We have hr,s,t=ln3r+6s+9t at 1,1,1 in the direction of v=4i+12j+6k

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

A: This is a problem of Vector Calculus.

Q: Q1:(A) What is the angle between the normal vectors to the curve F (1) = (2x² + x + 1)i + (+1)j +rk…

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Q: Let g(x, y) = e*^2 -vy (a) Find the directional derivative of g at (1, 1) in the direction of the…

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Q: Find the derivative of the vector function r(t) = ta x (b+ tc), where a = (4, -1,5), b = (-3,-3,-1),…

A: Given, the vector function      r(t)=ta×(b+tc),where       a=4,-1, 5, b=-3,-3, -1, and  c=1, 2, 2,…

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

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

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Q: Find the derivative, r'(t), of the vector function. r(t) at cos(2t)i + b sin5(t)j + c cos³ (t)k…

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 6t – t3, In(t))

A: Solution-  Given vector function  r(t) = (e-t, 6t-t3, ln (t)) We have to differentiate these…

Q: a) Find the directional derivative f (x, y, z) = x In(y+z) at point P (2, e, e) in the direction of…

A: We have to find directional derivative of vector f in the direction of vector v:

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 4t - t, In(t) r'(t)

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Q: For f(x,y,z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: Since there are two questions posted, we will answer the first question posted (1). If you want the…

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

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

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Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, 3, 2), b = (1,2,…

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

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Q: Find the derivative of the vector function ta x (b tc), where r(t) = (-1,1,-2) а %3 (-2,3, -1), ь 3…

A: Given vector function is,