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Find f x and f y. f ( x, y ) = x 5 + y 5 + x 5y

1. 2. 3. 4. Find f x and f y. f ( x, y ) = x 5 + y 5 + x 5y. f x = 5x 4 + 5x 4y, f y = 5y 4 + x 5 f x = 2x + 2xy, f y = 2y + x 2 f x = 3x 2 + 3x 2y, f y = 3y 2 + x 3 f x = 4x 3 + 4x 3y, f y = 4y 3 + x 4. 1. 2. 3. 4.

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Find f x and f y. f ( x, y ) = x 5 + y 5 + x 5y

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  1. 1. 2. 3. 4. Find f x and f y. f ( x, y ) = x 5 + y 5 + x 5y • f x = 5x 4 + 5x 4y, f y = 5y 4 + x 5 • f x = 2x + 2xy, f y = 2y + x 2 • f x = 3x 2 + 3x 2y, f y = 3y 2 + x 3 • f x = 4x 3 + 4x 3y, f y = 4y 3 + x 4

  2. 1. 2. 3. 4. Find the indicated partial derivatives. f ( x, y ) = sin ( 4x + 2y ) ; f y ( - 4, 8 ) • f y ( - 4, 8 ) = - 9 • f y ( - 4, 8 ) = 5 • f y ( - 4, 8 ) = 2 • f y ( - 4, 8 ) = - 8

  3. 1. 2. 3. 4. Find all the second partial derivatives. f ( x, y ) = x 4 - 9x 2y 3 • fxx = 2x 2 - 54y 3, fxy = - 54xy 2, fyx = - 54xy 2, fyy = - 54x 2y • fxx = 12x 2 - 18y 3, fxy = - 54xy 2, fyx = - 54xy 2, fyy = - 54x 2y • fxx = 2x 2 - 18y 3, fxy = - 54xy 2, fyx = - 54xy 2, fyy = - 54x 2y • fxx = - 12x 2 + 18y 3, fxy = 54xy 2, fyx = 54xy 2, fyy = 54x 2y

  4. 1. 2. 3. 4. If k, l, m are the sides of a triangle and K, L, M are the opposite angles, find {image} by implicit differentiation of the Law of Cosines. • {image} • {image} • {image} • {image}

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