Let f ( x , y ) = 3 x y + y 2. a) Find the directional derivative of f at (1,2) in the direction given by <1,1>. b) Find the second directional derivative of f at (1,2) in the direction given by <1,1>. (Don't follow a formula that you'll never remember! Just follow your nose...) c) What about the third directional derivative of f at (1,2) in the direction <1,1>? Please explain each step you make.

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A: To Find: Directional derivative

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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…

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

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A: The solution is given as

Q: (a) Find the directional derivative of f(z, y) = ry + y at the point (1,2) in the direction (1,1)

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A: Solved below

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Q: EXERCISE 2 Consider f(x, y) = 3x² – 4y² and U = %3D = cos î + sin r î. Use the Theorem above to find…

A: Here, the given function is: f(x,y)=3x2-4y2 which is differentiable. And, U→=cos 13π i^+sin 13π j^

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Q: EXERCISE 2 Consider f(x, y) = 3x² – 4y² and = = cos T î + sin 7 ĵ. Use the Theorem above to find the…

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Q: Find the directional derivative of f(x, y, z) = xy + z 3 at the pointP = (3, -2, -1) in the…

A: fx, y, z=xy+z3,  P=3, -2, -1. Now, ∂f∂x=y·1+0=y∂f∂y=x·1+0=x∂f∂z=0+3z2=3z2 Now, ∇fx, y, z=∂f∂x, ∂f∂y,…

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Q: 10. Let f(x, y) = x² + y³. Calculate the directional derivative of f in the direction of = (4, 3) at…

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Q: EXERCISE 2 Consider f(x, y) 3x2 · 4y² and U = cos r î + sin r ĵ. Use the Theorem above to find the…

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Q: Let f(x,y) = (x² + (G))°. Determine the directional derivative of f at the point (1,0) in the…

A: Explanation of the answer is as follows

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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…

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