Page 9. of 17 1 8) Given z =f (x,y)=1-(x² + 4y?) Find : a)The vector function, 10 normal to the surface of f at (x,y). b) Given: P (1,1) and Q (2, 2),Use the gradient to find the directional derivative of the function f at P in the direction of Q.

Q: 5. Find the directional derivative of f(x, y) = xy – y at the point (1, 2) along the unit vector…

A: The given function is: f(x,y)=xy-y2 Given point is: P = (1, 2) Direction vector is: v=3, 4

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

A: Hints: The given function is f(x,y)=-ylnx+xlny+xy The direction vector of a is a⇀a. Therefore 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: B A' A is the point (3, 1). Bis the point (a, 11). The gradient of AB is 5/½ 7 4

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Q: (a) Find the gradient of f . (b) Evaluate the gradient at the point P. (c) Find the rate of change…

A: The given function f(x,y,z)=xy+yz2+xz3, P(2,0,3)u=-23,-13,23

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: Given the function z= f(x, y) = ln(x² + xy - y²), find the following: a) Find gradient at the point…

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Q: 3-find the gradient of the function v if_w=(xy)/z at the point(1,-2,1), find the directional…

A: The answer provided below has been developed in a clear step by step manner.

Q: For each problem, calculate the directional derivative in the given direction and the gradient…

A: z=x2-6y2  To Find: Directional derivative and gradient vector at P(7,2) in the direction of  a)…

Q: f(x,y,z)=5sin(xyz), (a,b,c)=(1,1,π/4), and v⃗ =(3,-√2,3). Calculate the directional derivative…

A: Here we will evaluate each expression.

Q: For z = e"v In(ry): - Find the gradient of z when r= and y = 2 - Find the directional derivative of…

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Q: c) Find the directional derivative of f(x,y) = 10 – 3x2 + at P(2,–3) in the direction of the vector…

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