Let u(t) = 9t°i+ (-1)j-6k and v(t)=e'i+5ej- e5k Compute the derivative of the following function. u(t) - v(t) Select the corect choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the vector-valued function i+(Di+(k. O B. The derivative is the scalar function

Q: EX Prove that the directional derivative of f(x, y) = y² + 2xy³ + x²y² at point (0, 1) in the…

A: What is Directional Derivative: The directional derivative of a scalar function represents the rate…

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

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Q: 2. Find the directional derivative of o = yx2 +x²z + 3xyz in the direction of vector n = î + 2 ŷ -2·

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Q: Compute the derivative of the vector-valued function r(t)=⟨sin2t,et2⟩.

A: In order to compute the derivative of the vector-valued function: Differentiate the vector function…

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Q: The three components of the derivative of the vector-valued function u are positive at t = t0.…

A: Given: The three components of the derivative of the vector-valued function u are positive at t =…

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

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

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Q: Compute the directional derivative of the function g(x,y) = sin (x(4x – 5y)) at the point P(3, – 3)…

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Q: Find the directional derivative of the function f (x, y) = 7x² – 2.xy at the point P,(-3,5) in the…

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

A: Topic- Direction derivatives of function using partial differentiation .

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: 3. Prove that the directional derivative of f(x, y) = y² + 2xy³ + x²y² at point (0, 1) in the…

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Q: Find the derivative of the vector function r(t)=ta×(b+tc) where a=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and…

A: Solved below

Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: Since, you have posted multiple question. I am answering first one. Please post again with specific…

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: 12. Find the directional derivative of f(x, y, z)=zy+yz+xzat (1, 1, 2) in the direction of u =…

A: We can find the directional derivative in the following steps.

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 the function f(r, y) = 1+5x /j at the point (5, 1) %3D in the…

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Q: Find the approximation for the Green's function of the one-dimensional acoustic wave equation in the…

A: Given function is, cx=aebx Here, a>0 and it's constant here we have to see the effect of b so,…

Q: B. Find the directional derivative of the function f(x.y): X-y at the point (1.-1) Duts xy+1 in the…

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Q: Ex.: Find the directional derivative of the function f(x, y) x'y + x'y at the point (1,1) in the…

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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: 7. Find the directional derivative of the function f(x, y, z)=(y+28) at (2, 1, 1) in the direction…

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Q: Consider the function 422 + Vy+3z . f(x, y, z) = 3x – 7 Find the directional derivative of f at the…

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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 of function f(x y)=x°e' at the point (1,1) and direction of vector…

A: Given:       fx,y=x2ey    at the point 1,1 and direction of vector v=2i      fxx,y=∂∂xx2ey…

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

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Q: Find the second derivative of the vector-valued function #(t) = (6t + 4 sin(t))i + (5t + 7 cos(t))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: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

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 V…

A: Q1:   Given: f(x,y,z)=x3-xy2-2z with the point P0 (1,1,0)v=2i-3j-6kTo find:The directional…

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: 3. Consider the function f(r, y) = 'y - 4y at the point P(2,-1). (a) Find the directional derivative…

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

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Q: Q18:- Find the magnitude of the maximum and minimum directional derivatives of the function w = x -…

A: Given function is w=x2-3xy-y2+2xz2+6yz

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Q: The directional derivative of f(x, y) = xe + cosxy at P,(2,0) in the direction of the vector 3i - 4j…

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

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 the function f(x, y) = 1+5x/ at the point (5, 1) in the direction…

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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 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: Find the derivative of the vector function r(t) = (tan t, sec t,). %3D t2

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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: Find the derivative of f(x, y, z) = x3 - xy2 - z at the point po (2,1,0) in the direction of vector…

A: Given the function f(x, y, z)=(x3-xy2-z).........(1) We have to find the derivative of the function…

Q: Compute the directional derivative of the function f(x,y) = - xy + y at the point P(0, - 9) in the…

A: Solution-

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

A: First I have written the definition of directional derivative in the direction of unit vector.To…

Q: (b) Find the directional derivative of the function f(x,y,z) = xy sin z at the point (1,2, %3D T2)…

A: Solution:

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,

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.