If u and v are differentiable vector functions, c is a scalar, and f is a real-valued function, write the rules for differentiating the following vector functions. (a) u(t) + v(t) (b) cu(t) (c)f (t) u (t) (d) u(t) . v(t) (e) u(t) x v(t) (f ) u (f (t))

Q: 1. f(x, y) = 1+ 2x/y, (3,4), v= 4î – 3ĵ |

A: According to our company policy we can answer only first question and rest can be reposted. Thanks

Q: Find the derivative of the vector function r(t) = ta x (b+tc), where а 3 (—3, —4, — 2), b — (—2, —5,…

A: Topic:- vector and it's derivatives

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

A: The objective of the question is evaluate the directional derivative at the given point and…

Q: Find the domain of the vector-valued function

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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…

Q: State whether the following derivatives of vector-valued functionsr1(t) and r2(t) are scalars or…

A: To find:  whether the derivatives of vector-valued functions r1(t) and r2(t) are scalars or…

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

A: The given function is fx,y=7exsiny.    point: 0,π3   and   direction vector: v=-10, 24. Obtain the…

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

A:

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If Ř(0) = (-1,4,-5),…

A:

Q: Identify the vector-valued functions from the list below. O 6 (y) = y6 – 13e k (q, r, s) = In (13qr)…

A: A vector valued function is a function whose domain is a subset of real numbers and the range is a…

Q: 6.Consider a function f: R2 R, where f(xy) = cos(xy). Let u = be a unit vector. Use the definition…

A: Here we will use Definition of Directional derivative of f(x , y) in the direction of vector <u1…

Q: 6. Use a property of derivatives of vector valued functions to show that # [F(t) × F'(t)] = F(t) ×…

A: to show ddtrt→×rt→'=rt→×rt→'' we will use  ddtu→×v→=u→ddtv→+v→ddtu→

Q: Consider the function f (x, y) = 3 + 5x2 + 2y2, which is differentiable in an environment D from…

A: Given f (x, y) = 3 + 5x2 + 2y2

Q: Given the vector-valued function 7(t) =

A: Given,           r⇀(t)= < cos t, 3t, 2sin(t) >

Q: Consider the vector-valued function [f(x, y) xt – xy² [g(x, y) 2 Vx + y³x² [f(x, y) Which of the…

A: Find the Jacobian of the given matrix

Q: The directional derivative of f(x, y) = -xe²y – x³y at the point (0, 4) in the direction of the…

A:

Q: plain how to compute the derivative of r(t) = (f(t).g(t).h(t) oose the correct answer below. A. The…

A: In this question we have given a function in the form of vectors and we have to find its derivative.…

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

A: Givenf(x,y)=xx2+y2 , (2,1) , v=<3,5>

Q: If Ū is a unit vector and Di f(x, y) = 0 for all points (x, y) then f is a constant function..

A: We have to determine whether the following statement is true or false : If U→ is a unit vector  and…

Q: Let r(t) be a vector-valued function such that the magnitude of r(t) does not change over time. Use…

A: if r'(t) = 0 then we can say that r'(t) is perpendicular to the function r(t) for all times t.

Q: Example: Find the direction derivative of the function F(x,y,z)=x2 + y2+ z² at point p.(1,1,1)in the…

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Q: Let R be a differentiable vector-valued function such that R'(t) = (3t2, 2tvt2 + 1, 2t + 3) and R(1)…

A:

Q: Find the directional derivative, fv, of the function f (x, y) = 7+ x/] at the point P(1, 9) in the…

A: Directional derivative is the dot product of the normalized vector and gradient.It is denoted by fv

Q: Find the domain of the vector-valued function. (E r(t) = V 25 - t2i + t²j - 2tk tj- 2tk

A: Solution by using definition :

Q: #1. Find the directional derivative of the function f(x,y,z) = x²y + 2y2z at the point (1,–2,0) in…

A: Given:

Q: If F(x,y) is a differentiable function and the equation F(x, y) = 0 defines (y) as a function of…

A:

Q: (4)Find the scalar function such that F = V ø y i+ where F=- *+y x+y

A: We can find scalar function ϕ such that F→=∇ϕ ;where ∇ =i^∂∂x+j^∂∂y+k^∂∂z

Q: Why is r(t) = (f(t),g(t).h(t)) called a vector-valued function? %3D

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Q: Find the directional derivative of the function h at the point (1,1,1) in the direction of vector…

A:

Q: Is the vector valued function continuous at t=3? Defend your answer. I² -9 t- 3 V3t – 1, In(4 – t),…

A: Topic = Continuity

Q: Consider the function Question 1 f(x, y) = -y ln x + x lny + x y a) Find the directional derivative…

A:

Q: Given that the directional derivative of f(x ,y, z) at the point (3,-2,1) in the direction of a = 2i…

A: Given: f(x,y,z) at the point (3,-2,1) in the direction of a=2i-j-2k is -5 and that ∇f3,-2,1=5

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:…

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

Q: Let v = (3,4, 12) . Find the directional derivative of f(x,y, z) = x – y² +3z³ in the direction of…

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

A:

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

A:

Q: If r and u are differentiable vector-valued functions of t, then r(t) - u(t)) = r'(t) - u'(t). O…

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Q: c that make the convolution equal to zero for the vector function F(x, y, z) = (2az + y – 5x)i + (2x…

A:

Q: (1) Give an example of a function z = f(x, y) and a unit vector i such that f(0,0) = 2, fy(0,0) = 1…

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Q: Find the work done by the force F (x; y) = xyi-(y-x)j over the straight line from (1,1) to (2,3)

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

A:

Q: 2. Given f(x,y)=x(y-1)² (a) What is the directional derivative of fat (2,3) in the direction of the…

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Q: the directional derivative of f(x,y) = y^4+2xy^3+x^2y^2 at point (0,1) in the direction v = i +j is…

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Q: Suppose directional derivatives of the scalar function f(P), at a point P = (x, y), in 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 derivative of the vector function r(t) = ta x (b + tc), where a = (-5, 3, 2), b = (1,2,…

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

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.