Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) = x₂ using the following values. [:] A = x(t) = 4 - 17 1 -4 f(t) = 8t 4 , x(0) = At cost + 4 sint sint - 17 sin t cost-4 sint ...

Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: I. Find the second derivative 3. y = (x +8) (6x-1)

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Q: If f(0) = sin 0 = 0.1, find f(0 + 7).

A: fθ=sinθ =0.1

Q: Given f"(x) =| 16 sin(4x) and Find f

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Q: If f(x) = 18x2 + 96 3 ³√√x' find f'(8).

A: Given Function:- fx=18x23+96x3

Q: rom the solution provide on #9, how did you get from the 2nd derivative 2 - 2/t3 =0  to 1-1/t3 =0?

A: To explain how to get from the 2nd derivative 2 - 2t3 =0  to 1-1t3 =0

Q: If f(x) = 18z + 9, find f'( – 1).

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Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

Q: 3) Find the following derivatives: a. y = 2x b. f(x) = 4x³10x² + 7x-15 c. g(x) = 3x(x² - 4)5 d. y =…

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Q: Find the 10th derivative of y = cos 3x. f(10)(x) =

A: Given, y=cos3x

Q: 1) Find the derivative of f(x)= 2x³+ 2x +12. Then evaluate the

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…