3) Find the partial derivatives f and fy for the functions: 4 i. f(x, y) = cos-. ex²-5y³. ii. f(x, y,z) = x'y + 10x'y²+ 43x- ztan 4y. %3D

Q: Prove or disprove: There exists an integer a such that 14 | (3a — 5) and 21 | (2a + 3).

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Q: la 이 If A = 1 1l and B = 15 11, then A² = B if a = ?

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Q: Find both first partial derivatives. h(x, y) = e-(x9 + y9) h,(x, y) = h,(x, v) =

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Q: Find the second-order partial derivative. Find fy 2x. when f(x,y) = 8x y-7y+ 3. xy O A. 48xy O B. -…

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Q: dy for the following implicit functions : dx Find a) x+4xア-ア 5y =3 3べ+5y'x"+4\」 (ans.: 2.x 10xy-y

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Q: Find partial derivative.

A: We use product rule to find the partial differentiation.

Q: Please help. *Find fzxy; f(x,y,z) = x⁵y⁸z⁴+y⁴z. *The partial derivative of z = sin(7x³y+8xy²) is;

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Q: Q1: Find partial derivatives of the function with respect with each variable 4) f(x, y) = Vx² + y²…

A: We find the partial derivatives of the given function f(x, y)=x2+y2, by using the definition of…

Q: Calculate the partial derivatives and using implicit differentiation of (TU – V)? In (W – UV) = In…

A: We will find out the required values.

Q: What is the result of the partial derivative 3(z² + y sin (z)) Select one: a. 2a + y * cos(x)

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Q: Q1: Find partial derivatives of the function with respect with each variable 6) r(x, y) = In(x+ y)

A: The detailed solution is as follows below:

Q: Find all the second partial derivatives. f(x, y) = x6y − 3x3y2

A: