Suppose y = A cosh (11) + B sinh (11x), and A and B are arbitrary constants. If you are not familiar with the hyperbolic functions, cosh (x) = **te, sinh (x) = But the only facts you need for this problem are cosh' = sinh and sinh' = cosh. 2 Find the following. Y (x) = y" (x) = If possible, rewrite your answer to the previous part in terms of y only: y" (x) = %3D Give a two-parameter family of solutions of the differential equation da 121y . Use A and B as the names of the parameters. y =

Q: = 5x² + 3x + xy = 5 and y(5): = 27, find y' (5) by implicit differentiation.

A: Given query is to find the derivative at indicated point.

Q: ent's Tents has four red tents and three green tents in stock. Karin selects four of them at random.…

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Q: Use standard derivatives and differentiation rules to find for each of the following. dx If…

A: We have to find derivative

Q: Find the formula for a parabola with its vertex at (9,4) and with a second derivative of -3. f(x)=

A: let's equation of parabola is given by y=ax2+bx+c                                              ..1…

Q: Given xy + 2x + 3x² = 1: (a) Find y' by implicit differentiation (leave your answer in terms of x…

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Q: Find any relative maxima and relative minima. relative maximum (x, y) = relative minimum (x, y): %3D…

A: The given function is - y = x(x-5)2y' = -x+5(x-5)3y'' = 2x+20(x-5)4

Q: Find y" by implicit differentiation. 2x3 + 5y³ = 2 y" = 2x² 512 X

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Q: Find y as a function of x if x²y" – 3xy' + 4y = x", y(1) = 3, y'(1) = –5. y =

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Q: Suppose f(4) = -1 and f'(4) = -10. An object moves along the curve y³ - 2x² f(x) - 2x = 51. For a…

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Q: For each problem, find the function f based on the information given. 13. f'(x)=√x(6+5x) 14.…

A: 13) Given:  f'(x) = x6+5x ⇒f'(x) = 6x12+5x32 Integrate both sides with respect to x we get

Q: p(x) = (e³x+5 + n)³. q(x) = In(5e* + 6 tan x). u(x) = e*In(x)-x+2.

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Q: If x2 + y? = x³y3 + 1, use implicit differentiation to find y' at the point (1, 1).

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Q: (4) (3) (4) e. y = 4x³ (2x + 7) 4 f. y = 1 5√√(3-15x)³ g. s = 8cos (4t2 +9) ...determine s' s'(2)

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Q: The curve y = ax + bx + c passes through the point (1,8) and is tangent to the line y = 5x at the…

A: Given that: y=ax2+bx+c passes through (1, 8) and tangent to line y=5x at origin.

Q: y as a function of x if '(1) = −2. x²y" +19xy' +81y = x5,

A: Given that the differential equation is                                      To find 'y' as function…

Q: Find the derivative y' for each of the following curves or functions. You do not need to simplify…

A: Given Expression: y=1x3-2ln(x)+5x4        .........(1) y=ex-4x-3(2+x     .........(2) y=2x2-4x+17x+4…

Q: 2. Find the derivatives of the following functions. 4 a. f(x) = 3x³ x2 b. f(x) = (4 – x²)" C. f(x) =…

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