Consider the functions f(x, y) = xy, x(r, 0) = rcos(0), y(r, 0) = rsin(0). %3D (a) Compute the two partial derivatives of the composition f(x(r ,0), y(r, 0)) using the chain rule. (Hint: Your answer should only involve r and 0) (b) Compute the two derivatives of the composition f(x(r, 0), y(r, 0)) by calculating the composition and then computing the partials of the result. (Hint: Your answer should agree with part (a)).

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A: Solution of first partial derivatives.

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y - 5xyz + 7yz?…

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A: This question is related to differentiation, We will solve it using given information.

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 2xyz + 9yz2…

A: The solution is given below in the next step:

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 6xyz + 10yz? %3D…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 8xyz + 7yz?…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y – 6xyz + 10yz?…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 6xyz + 10yz %3D…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 6xyz + 10yz? %3D…

A: topic - partial derivatives

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y – 5xyz + 10yz?…

A: We will solve the problem

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x2y – 6xyz + 10yz?…

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Q: 1)Consider the function f(x, y) = x° + 2xy + y? – 5x b) Calculate the second-order partial…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y – 5xyz + 9yz?…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 9xyz + 6yz²…

A: The objective of the question is determine the partial derivative.

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Q: Differentiate implicitly to find the first partial derivatives of z. x In(y) + y2z + z? = 33 dz ax…

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Q: Find the first partial derivatives of the function. f(x, у) : cos(t5) dt fx(x, y) = fy(x, y) =

A: We use the leibniz derivative.