Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=x₂ using the following values. -2 sec (t) ^-[-]-[-2]-[:] ,f(t) = 0 A = At= || 01 10 cos (t) sin(t) sin (t) cos (t) x(0) = x(t) = (Use parentheses to clearly denote the argument of each function.)

Q: Given f''(x) = - 36 sin(6x) and f'(0) = 6 and f(0) = 0. 70 Find f)

A: Given that      f"(x)= -36sin(6x) , f'(0)=6 and f(0)=0 .

Q: If H(0) = 0 sin 0, find H'(0) and H"(0). %3D H'(0) =

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Q: If f(x) = 3x sin cos x, find f'(x)=-4.88 To two decimal places, Find f'(2) = -7.21 X

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Q: ) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)? Consider the function f(x) whose second…

A: Given:

Q: csc(x) – 1 sec(x) Differentiate: f (x) = (A f'(x) = - csc²(x)+ sin(x) B B f'(x) = - csc2(x) – cos(x)…

A: We can use differentiation of trigonometric function rules to find the derivative of the given…

Q: Given f''(x) = - 16 sin(4x) and f'(0) Find f ¹ƒ(3/3) = = 6 and f(0) = - 5.

A: SOLUTION-

Q: f(x) = ln(cos3(2x+1)5)     f'(x) = ?

A: Given that f(x) = ln(cos3(2x+1)5)

Q: If f(x) = sin(x³), find f'(x). 3x² cos(x³) Find f'(2). ४ OF

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Q: Given f''(x) = = Find 76 10 - - 36 sin(6x) and f'(0) = 2 and ƒ(0) = − 6.

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Q: find y'. (show all the steps please) cos(xy) = x-y^2

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Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: Given f''(x) = 25 sin(5x) and f'(0) = 3 and f(0) = 6. - Find f() = 6

A: Given that  f"(x) = - 25.sin(25x)......   (1) f'(0) = 3 f(0) = 6 To find  fπ6

Q: y''+y=(1)/(cos(x)) Solve

A: Consider the provided differential equation,

Q: Find (i) the first derivative of f(x) = 3 x³. Inx + 5 e*. sin-1x + tan-1(4x) (ii) the second…

A: To find the following parts,

Q: If f(x) = 5 sin−¹(x³), find ƒ'(x). 15x² cos(x³) sin(2³)² x3 Find f'(0.4). X

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Q: Ql:- Find the domain of the following functions a) S(x) = sin"*(2 – 3x) b) f(x) = sec"*(x – 2)

A: we have to find domain

Q: If f(x) f'(x) = f'(4) = = 4 sin x 3 + cos x " then

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Q: Suppose f(pi/3) = 5 and f'(pi/3) = -7, and let g(x) = f(x

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Q: Given f'(x) = 6 cos x - 10 sinx and f(0) = -5, O find f(x) C

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Q: We have an unknown function f(x) which satisfies    f''(x) + f'(x) -2f(x) = x2 The first term is the…

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Q: If g(x) = cos(x) then g'(x) = = g'(1) = -sin(x)

A: NOTE: Refresh your page if you can't see any equations. . take derivative…

Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

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Q: If f(x) = 7cos(x), what is f'(x) ?

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Q: Suppose that f(4) = 2 and f' (4) = h(x) = (2x² + 3in (f(x)))² h' (4) = (b) h(x) = 20f(x) e-2x + 3…

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Q: Find f. f(x) = f"(x) = 5ex - 7 sin(x), f(0) = 3, ( 77 ) = 0 EN 2

A: Given :f''x=5ex-7sinx

Q: Find f'(x) = = 4-5 sin(x) cos²(x) f(x) = -4 sin(x) + 5 cos(x)

A: Given : f(x)=-4sin(x)+5cos(x)   To Find : f'(x)

Q: Given f’(x)= 3 cos x - 9 sin x and f(0)= -6 find f(x)

A: We can solve this as follows:

Q: -3 tan x, then f'(x) = -sin(x) - 3 sec²(x) To two decimal places, = COS X f'(2) = - HI

A: